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1 Number Sense and Operations representing as they: 6.N.1 6.N.2 6.N.3 6.N.4 6.N.5 6.N.6 6.N.7 6.N.8 6.N.9 6.N.10 6.N.11 6.N.12 6.N N.14 6.N.15 Demonstrate an understanding of positive integer exponents when used in powers of ten. Demonstrate an understanding of fractions as a ratio of whole numbers. Identify and convert between mixed numbers and fractions. Find and position integers, fractions, mixed numbers and decimals both positive and negative on a number line. Compare and order integers, including negative integers and positive fractions, mixed numbers, decimals and percents. Apply number theory concepts, including prime factorization, greatest common factor and least common multiple to the solution of problems. Select and use appropriate operations to solve problems involving addition, subtraction, multiplication, division and positive integer exponents with whole numbers, fractions, mixed numbers, decimals and percents. Apply the order of operations for expressions involving addition, subtraction, multiplication and division with parentheses Demonstrate an understanding of the inverse relationship of addition and subtraction and use that understanding to simplify computations and solve problems Accurately and efficiently add, subtract, multiply and divide with double digit divisors and positive decimals Accurately and efficiently add, subtract, multiply and divide positive fractions and mixed numbers. Simplify fractions. A. Convert improper fractions to mixed numbers B. Find equivalent fractions Add and subtract integers, with the exception of subtracting negative integers Use the number line to model addition and subtraction of integers Estimate the results of computations with whole numbers, fractions, mixed numbers, decimals and percents. Describe the reasonableness. Translate between scientific notation and standard notation for large and small numbers APS Math Benchmarks Page 1 of 5
2 Pattern, Relations, and Algebra 6.P.1 6.P.2 6.P.3 6.P.4 6.P.5 Evaluate algebra variable expressions with given values and simplify 3x-Y Use the properties of equality to solve one-step equations Represent real situations and mathematical relationships with concrete models, tables, graphs and rules in words and symbols Produce and interpret graphs that represent the relationship between two variables in everyday situations Identify and describe relationships between two variables with a constant rate of change. Contrast these with relationships where the rate of change is not constant. APS Math Benchmarks Page 2 of 5
3 Geometry 6.G.1 6.G.2 6.G.3 6.G.4 6.G.5 6.G.6 6.G.7 6.G.8 6.G.9 Identify polygons based on their properties including types of interior angles, perpendicular or parallel sides and congruence of sides Identify three-dimensional shapes (e.g. cubes, spheres, prisms and cones) based on their properties such as edges and faces Identify relationships between points, lines and planes, (e.g. intersecting and parallel) Graph points and identify coordinates of points on the Cartesian Coordinate Plane, (all four quadrants) Find the distance between two points on a horizontal or vertical number line Predict, describe and perform transformations on two-dimensional shapes, (e.g. rotation, translation and reflection) Identify types of line and rotational symmetry Determine if two shapes are congruent by measuring sides or a combination of sides and angles or by a series of motions, (e.g. rotations and reflections) Match three-dimensional objects with their two-dimensional representations. APS Math Benchmarks Page 3 of 5
4 Measurement 6.M.1 6.M.2 6.M.3 6.M.4 6.M.5 6.M.6 6.M.7 Use formulas for calculations of area and perimeter Identify, measure, describe, classify and construct various angles, triangles, and quadrilaterals Solve problems involving proportional relationships and units of measurement, (e.g. scale models and maps) Find areas of triangles and parallelograms. Develop strategies to find area of more complex shapes. Identify, measure and describe circles and the relationships of circumference and area and use concepts to solve problems Find volume and surface areas of rectangular prisms Find the sum of the angles in simple polygons (up to eight sides) with and without measuring the angles. APS Math Benchmarks Page 4 of 5
5 Data Analysis, Statistics, and Probability 6.D.1 Use tree diagrams and other models such as lists and tables to represent possible or actual outcomes of trials. Analyze the outcomes 6.D.2 Predict the probability of outcomes of simple experiments (e.g. tossing a coin or rolling a die) and test the predictions 6.D.3 Use appropriate ratios between 0 and 1 to represent the probability of the outcome and associate the probability with the likelihood of the event APS Math Benchmarks Page 5 of 5
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Content Strand: Number and Numeration Understand the Meanings, Uses, and Representations of Numbers Understand Equivalent Names for Numbers Understand Common Numerical Relations Place value and notation | 7,448 | 33,264 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.375 | 4 | CC-MAIN-2018-34 | longest | en | 0.860089 |
http://www.pearltrees.com/u/17165570-woodlands-maths-interactive | 1,716,142,144,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971057819.74/warc/CC-MAIN-20240519162917-20240519192917-00556.warc.gz | 51,587,369 | 23,104 | # Woodlands Maths Zone - Fun interactive maths games
Mathematics Fun, Fact, Fiction, Function, Fantasy Here is a collection of mathematical activities and curiosities...enjoy them! BRAND NEW 2008 Line of Fractal Imagery -- 594 Images -- Oh Wow! ---> Show me the fractals! Extensive Graphical Spherical Harmonic Study --- 640+ Images ---> Take me there! 2006 Line of Fractal Imagery -- 336 Images -- Gotta See Them ---> Let's go there! Guess Your Birthday! Here's a fun trick to show a friend, a group, or an entire class of people. Step 1) Have them take the month number from their birthday: January = 1, Feb = 2 etc. Have them give you the total. How It Works: Let M be the month number and D will be the day number. Thus, if you subtract off the 165, what will remain will be the month in hundreds plus the day! By the way, if you wish to know how many minutes and seconds you have been alive and lots more about when you were born, you might like to try this website ==> Birthday Calculator Divisibility Rules! *A big thank you to Torsten Sillke for these rules! Do You Love "Alphametics?" Did You Know?
The Thirty Greatest Mathematicians Click for a discussion of certain omissions. Please send me e-mail if you believe there's a major flaw in my rankings (or an error in any of the biographies). Obviously the relative ranks of, say Fibonacci and Ramanujan, will never satisfy everyone since the reasons for their "greatness" are different. I'm sure I've overlooked great mathematicians who obviously belong on this list. Following are the top mathematicians in chronological (birth-year) order. Earliest mathematicians Little is known of the earliest mathematics, but the famous Ishango Bone from Early Stone-Age Africa has tally marks suggesting arithmetic. Early Vedic mathematicians The greatest mathematics before the Golden Age of Greece was in India's early Vedic (Hindu) civilization. Top Thales of Miletus (ca 624 - 546 BC) Greek domain Thales was the Chief of the "Seven Sages" of ancient Greece, and has been called the "Father of Science," the "Founder of Abstract Geometry," and the "First Philosopher." Tiberius(?)
Percents and Decimals Worksheets Thanks for visiting the U.S. number format version of the decimals and percents worksheets page at Math-Drills.Com where we make a POINT of helping students learn. On this page, you will find Decimals worksheets on a variety topics including comparing and sorting decimals, adding, subtracting, multiplying and dividing decimals, and converting decimals to other number formats. To start, you will find the general use printables to be helpful in teaching the concepts of decimals and place value. Further down the page, rounding, comparing and ordering decimals worksheets allow students to gain more comfort with decimals before they move on to performing operations with decimals. General Use Printables The thousandths grid is a useful tool in representing operations with decimals. Thousandths GridHundredths GridsDecimal Place Value Chart Expanded Form with Decimals Rounding Decimals Worksheets The convention on the decimals worksheets below is to round up on a five. Percents Worksheets
Connecting to Math in Real Life By Wendy Petti Who needs math games when a world of meaningful real-life fun is beckoning? It's easy and rewarding to connect to the real world in math class. Collections of Real-World Math Activities The math activity sites listed here are repositories of lesson ideas that can be explored offline without the use of computers. Math Goodies Their multi-media curriculum includes 168 in-depth lessons organized into instructional units. Practical Uses of Math and Science (PUMAS) This site offers 71 examples of real-life applications of math for upper elementary grades and above, including drawing/interpreting topographical maps, money math, creating math magic problems, measuring the heat of sand and rock; and much more. Mixing in Math This set of free activities helps teachers, parents, and after-school programs mix a bit of math into students' daily routines. National Math Trail Students from around the United States created real-life word problems related to their communities.
Multiples and Factors In this activity, students identify multiples and factors and solve problems that involve finding highest common factors and lowest common multiples. Students will need a good recall of multiplication basic facts in order to be able to do these activities. Activity One and Game Discuss the definitions of multiples and factors (on the student book page) before your students begin this activity. Make sure that they understand that every number is a factor of itself, because if they divide a number by itself, there is no remainder. This game could be extended by asking: • What are all the different products you could throw with the two game dice, one labelled 1–6 and the other 4–9? • There are two different ways of getting a product of 12: throwing a 3 and a 4 or a 2 and a 6. • What’s the probability of throwing a double? • Which squares in the game are easier/harder to cover? Harder to cover: a prime number [only 2 out of 36 combinations] and a multiple of 7 [only 6 chances out of 36].)
Math Projects About Project-Based Learning Projects help students personalize their learning and are ideal for gaining key knowledge and understanding of content and answering the question: Where am I ever going to use this?" Among the greatest benefits of project-based learning (PBL) are gains in students' critical-thinking skills and development of their interpersonal and intrapersonal skills. However, as Bryan Goodwin (2010) found in reviewing the literature, a major shortcoming in many student projects is that educators tend to assign projects just for the sake of doing them. Students should publicly present their work, as they will be more motivated to produce a quality product when knowing a real audience will view it (Larmer & Mergendoller, 2015, 2010). If projects involve teamwork, educators will need to emphasize commitment to the team as an essential component for success of group work. Finally, projects should include the element of reflection. Key Questions Scaffold projects. Yetkiner, Z.
Murderous Maths: Tricks and Games! Do you want to be a mind reader? Or maybe have a brain that does lightning calculations? Or maybe you just want to make your friends feel silly! Here are a few of my sneakiest tricks, and don't worry - you don't need to be a maths genius to do them! Some of these tricks are in the Murderous Maths books, but here I can let you play on my special calculators and other computer gadgets! The Fiendish Football Team Illusion! Let Riverboat Lil READ YOUR MIND! The EIGHT QUEENS Puzzle! The 7-11-13 Trick (And other miracle sums) Pass your friends a calculator - and then make them feel really silly with these simple tricks! The Predictor Cards The trick with four cut-out cards, you pick a number from 1-16 and it mysteriously appears in a hole at the back! The Missing Digit Trick Your friend does a sum then crosses a digit out - you can tell what it is without looking! The Prime Numbers Trick Make a strange prediciton using the magic of PRIME NUMBERS. What were you like when you were born? | 1,546 | 7,260 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.09375 | 3 | CC-MAIN-2024-22 | latest | en | 0.923021 |
https://qa.answers.com/Q/How_many_1200_milligrams_in_tsp | 1,696,160,093,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510888.64/warc/CC-MAIN-20231001105617-20231001135617-00491.warc.gz | 518,242,643 | 43,919 | 0
# How many 1200 milligrams in tsp?
Updated: 4/28/2022
Wiki User
7y ago
Milligrams can't be converted to teaspoons. Milligrams measure mass, while teaspoons measure volume.
Wiki User
7y ago
Wiki User
8y ago
There are 5 milligrams in 1 teaspoon, so there are 240 teaspoons in 1200 milligrams. | 88 | 302 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2023-40 | latest | en | 0.872698 |
https://help.simetrix.co.uk/8.1/simetrix/script_manual/topics/func_truncate.htm | 1,563,857,558,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195528869.90/warc/CC-MAIN-20190723043719-20190723065719-00337.warc.gz | 403,416,778 | 35,669 | # Truncate Function
Returns a portion of the input vector with defined start and end points. Interpolation will be used to create the first and last points of the result if the start and end values do not coincide with actual points in the input vector.
Arguments 2 and 3 define the beginning and end of the vector.
### Arguments
Number Type Compulsory Default Description 1 real array Yes Vector 2 real No start of vector Start x value 3 real No end of vector end x value
### Returns
Return type: real array
### Example
Suppose we have a vector called VOUT which was the result of a simulation running from 0 to 1mS. We want to perform some analysis on a portion of it from $250\mu$S to $750\mu$S. The following call to Truncate would do this:
Truncate(VOUT, 250u, 750u)
If VOUT did not actually have points at $250\mu$S and $750\mu$S then the function would create them by interpolation. Note that the function will not extrapolate points before the start or after the end of the input vector. | 243 | 1,004 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2019-30 | latest | en | 0.839136 |
https://www.freemathhelp.com/forum/threads/volume-of-the-solid-plane.121351/ | 1,591,466,160,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590348517506.81/warc/CC-MAIN-20200606155701-20200606185701-00249.warc.gz | 696,999,107 | 14,277 | # Volume of the solid plane
#### ozgunozgur
##### New member
Hello there, can you help me to solve this problem? Thanks.
#### Attachments
• 36.1 KB Views: 10
#### Prof
##### Junior Member
You need to submit an attempt at solving the problem, and we can help you where you are stuck. In the mean time, I can get you started.
In both parts, start by making a graph of the 3 equations and shade the region that is bounded by them.
Then both questions can be solved using the disk method for volume.
#### ozgunozgur
##### New member
You need to submit an attempt at solving the problem, and we can help you where you are stuck. In the mean time, I can get you started.
In both parts, start by making a graph of the 3 equations and shade the region that is bounded by them.
Then both questions can be solved using the disk method for volume.
Should I rotate it separately for three of them?
#### Attachments
• 2.2 MB Views: 1
#### MarkFL
##### Super Moderator
Staff member
Let's look at a graph of the region to be revolved:
For part (a), I would use the washer method, where the outer radius $$R$$ is the parabolic function and the inner radius $$r$$ is the linear function. Can you give the volume of an arbitrary washer?
$$\displaystyle dV=\pi(R^2-r^2)=?$$
#### ozgunozgur
##### New member
I don't know if this is true. Thanks
#### Attachments
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#### MarkFL
##### Super Moderator
Staff member
For part (a) we are revolving about the $$x$$-axis. I would write:
$$\displaystyle dV=\pi((x^2+4)^2-(4x)^2)\,dx=\pi(x^4-8x^2+16)\,dx$$
Now integrate over the appropriate boundaries. What do you get?
I did
#### Attachments
• 1.1 MB Views: 2
#### MarkFL
##### Super Moderator
Staff member
You found the anti-defivative of the integrand, but you need to evaluate a definite integral.
#### ozgunozgur
##### New member
You found the anti-defivative of the integrand, but you need to evaluate a definite integral.
Sorry but I didn't understand which boundaries I need to take. Could you solve all?
#### MarkFL
##### Super Moderator
Staff member
Look at the diagram I posted above. We are essentially revolving vertical strips about the $$x$$-axis, where these strips are bounded by the two given functions (quadratic is top boundary, and linear is bottom boundary). The width of each strip is $$dx$$. What is the smallest and largest value for $$x$$ over which we are adding washers (integrating)? Can you express the volume as a definite integral and then use the FTOC to compute the value?
You need to be able to do this yourself, as I am happy to guide you, but you'll learn very little if I just provide the answers.
#### ozgunozgur
##### New member
I wonder. Must the smallest and largest value be equal to the zero and eight like this or the strips are already those functions? However, I like to learn with examination solvings. And I don't want to keep you hours here.
#### Attachments
• 2.2 MB Views: 1
#### MarkFL
##### Super Moderator
Staff member
No, the strips run from $$x=0$$ to $$x=2$$. We are given the lower bound, since the vertical line $$x=0$$ is one of the boundaries of the shaded region. The upper limit fomrs from there the quadratic and linear functions intersect:
$$\displaystyle x^2+4=4x$$
$$\displaystyle x^2-4x+4=0$$
$$\displaystyle (x-2)^2=0\implies x=2$$
Hence:
$$\displaystyle V=\pi\int_0^2x^4-8x^2+16\,dx=\frac{256}{15}\pi$$
#### ozgunozgur
##### New member
No, the strips run from $$x=0$$ to $$x=2$$. We are given the lower bound, since the vertical line $$x=0$$ is one of the boundaries of the shaded region. The upper limit fomrs from there the quadratic and linear functions intersect:
$$\displaystyle x^2+4=4x$$
$$\displaystyle x^2-4x+4=0$$
$$\displaystyle (x-2)^2=0\implies x=2$$
Hence:
$$\displaystyle V=\pi\int_0^2x^4-8x^2+16\,dx=\frac{256}{15}\pi$$
Thank you so much, sir. At the other part(y-axis), will the boundaries need again 0 and 2, and x will be equal to 2?
#### MarkFL
##### Super Moderator
Staff member
When revolving about the $$y$$-axis, I would use the shell method, where:
$$\displaystyle dV=2\pi x((x^2+4)-4x)\,dx$$
Do you see that the radius of an arbitrary shell is $$x$$ and the height is the difference between the quadratic and the line?
#### ozgunozgur
##### New member
When revolving about the $$y$$-axis, I would use the shell method, where:
$$\displaystyle dV=2\pi x((x^2+4)-4x)\,dx$$
Do you see that the radius of an arbitrary shell is $$x$$ and the height is the difference between the quadratic and the line?
I found 8 pi. Is this correct? What is the difference between washer and shell method?
#### Subhotosh Khan
##### Super Moderator
Staff member
I found 8 pi. Is this correct? What is the difference between washer and shell method?
Volume by washer method
Volume by shell method
Tell us what you found and tell us if you do not understand something in any of those references.
#### MarkFL
##### Super Moderator
Staff member
I found 8 pi. Is this correct? What is the difference between washer and shell method?
Let me check:
$$\displaystyle V=2\pi\int_0^2 x((x^2+4)-4x)\,dx=2\pi\int_0^2 x^3-4x^2+4x\,dx=2\pi\left[\frac{1}{4}x^4-\frac{4}{3}x^3+2x^2\right]_0^2=2\pi\left(4-\frac{32}{3}+8\right)=\frac{8}{3}\pi$$ | 1,506 | 5,252 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.78125 | 4 | CC-MAIN-2020-24 | latest | en | 0.91638 |
http://en.m.wikipedia.org/wiki/Type_rule | 1,369,149,099,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368700132256/warc/CC-MAIN-20130516102852-00029-ip-10-60-113-184.ec2.internal.warc.gz | 82,311,114 | 6,287 | # Type rule
In type theory, a type rule is an inference rule that describes how a type system assigns a type to a syntactic construction. These rules may be applied by the type system to determine if a program is well typed and what type expressions have. A prototypical example of the use of type rules is in defining type inference in the simply typed lambda calculus, which is the internal language of Cartesian closed categories.
## Notation
An expression $e$ of type $\tau$ is written as $e\!:\!\tau$. The typing environment is written as $\Gamma$. The notation for inference is the usual one for sequents and inference rules, and has the following general form
$\frac{\Gamma_1 \vdash e_1\!:\!\tau_1 \quad \cdots \quad \Gamma_n \vdash e_n\!:\!\tau_n}{\Gamma \vdash e\!:\!\tau}$
The sequents above the line are the premises that must be fulfilled for the rule to be applied, yielding the conclusion: the sequents below the line. This can be read as: if expression $e_i$ has type $\tau_i$ in environment $\Gamma_i$, for all $i=1..n$, then the expression $e$ will have an environment $\Gamma$ and type $\tau$.
For example, a simple language to perform arithmetic calculations on real numbers may have the following rules
$\frac{\Gamma \vdash e_1\!:\!real \quad \Gamma \vdash e_2\!:\!real}{\Gamma \vdash e_1+e_2\!:\!real} \qquad \frac{\Gamma \vdash e_1\!:\!integer \quad \Gamma \vdash e_2 : integer}{\Gamma \vdash e_1+e_2\!:\!integer} \qquad \cdots$
A type rule may have no premises, and usually the line is omitted in these cases. A type rule may also change an environment by adding new variables to a previous environment; for example, a declaration may have the following type rule, where a new variable $id$, with type $\tau'$, is added to $\Gamma$:
$\frac{\Gamma \vdash e'\!:\!\tau' \quad \Gamma, id\!:\!\tau' \vdash e\!:\!\tau}{\Gamma \vdash \text{let id = } e' \text{ in } e \text{ end} :\!\tau}$
This types can be used to derive composed expressions types, much like in natural deduction.
↑Jump back a section | 558 | 2,030 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 18, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.59375 | 4 | CC-MAIN-2013-20 | latest | en | 0.848959 |
https://club-keanu.com/how-to-calculate-solar-plant-performance-ratio-pr-solar-pv-design/ | 1,631,865,341,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780055601.25/warc/CC-MAIN-20210917055515-20210917085515-00461.warc.gz | 231,615,258 | 12,631 | # HOW TO CALCULATE SOLAR PLANT PERFORMANCE RATIO (PR) | SOLAR PV DESIGN
Hi Guys, welcome to Minutes 2 Energy. We are a team of Solar professionals with
more than 10 years of experience in technology and business fields and today we are going
to share our knowledge and experience with you. Please see the video till the end for useful
resources. So, let's start!! Today’s topic is Solar Plant Performance
Ratio or in short PR. PR is a very important tool or factor that
being used globally by companies and professionals to assess the healthiness of Solar PV system.
So let’s know how this PR is calculated
and how it is so important for Solar PV System. So what is Performance ratio or the PR for
Solar PV Power Systems? PR is the Ratio of Effective Produced Energy
to Ideal Energy Yield at STC Condition. As it’s a Ratio it is Unit less and globally
it is being denoted as a Percentage value. Here the term Effective Energy is the available
Useable Energy delivered to the Grid or to the End User. While calculating the PR all the losses like
Optical losses PV array Losses DC to AC conversion losses and the other System losses are taken
info on Different types of system losses.
Simple Annual PR measured on the basis of
Actual Annual useable energy and the Annual Solar Irradiance
Now let’s see the Formula of PR. So PR is equals to E Grid divided by the product
of GII and P Nom PV. Here E Grid is the Useable energy available
at the User End. Unit of E grid is kilo Watt hours per year. GII refers to the Global Inclined Irradiation
received by the Solar PV array at certain tilt angle. Next is P nom PV. This is Solar PV array’s installed DC capacity
and denotes as kilo Watt Peak.
Next is the types of PR which are there for
their own significance and applicability. So let’s know more about them. First is STC Equivalent PR. It is determined by adjusting the power at
each recording interval to compensate for difference between the actual PV module temperature
and the STC reference temperature. This method normally used when the System
PR is to be measured at a short duration of day time. Annual Temperature corrected PR is similar
to the previous one. Here PR is calculated by adjusting the reporting
period with respect to power to compensate for the difference between the actual PV module
Temperature and the expected annual average module temperature.
Annual Temperature correction is significant
when the Annual PR is required to be Validated for within 15 to 20 days of operation. Now let’s look at an example of how to calculate
simple annual PR with available plant operational data. For any given year and location say from a
one thousand kilo watt peak Solar PV On-Grid installation the annual Global Irradiance
received at the PV plane is 1875 kilo Watt hours per meter square per year and the useable
energy fed to grid is 1540 Mega Watt Hours. Now here the E grid is 1540 megawatt hours
or 1540 into 1000 kilo watt hours per year. GII is 1875 kilo Watt hours per meter square
per year and the P nom PV is one thousand kilo watt peak. Then the yearly PR Should be calculated as
1540000 divided by open bracket 1875 multiplied by 1000 close bracket. Which is 0.82 or 82%. So hope you now understand how to calculate
Annual Performance ratio of solar Plant. Please see our other video on How to Calculate
PR in MS Excel for more detailed understanding. The Solar Plant Performance Ratio is defined
in the norm IEC EN 61724.
61724-1 (2017 edition). Link to get the standard from IEC webstore
is in the description below. Now let’s talk about Few Points you should
keep in mind while assessing the Solar Plant Performance Ratio. First PR always represented as Percentage. Second PR is a Ratio of actual energy generated
to the ideal energy Yield for a given period. And the third one is that it is independent
of location’s specific Irradiance level. So What is the Significance of Plant Performance
Ratio? Well The PR is an important metric in the
PV industry it is often used as a contractual condition / contract warranty when commissioning
a PV system Irrespective Of System Size Or System Type whether be it ground-mount or
rooftop based Grid-connected or Off-grid be it a small rooftop system or even an Ultra
Megawatt utility scale solar plant.
Also we professionals always check PR for
the HEALTHINESS of the plant and to VERIFY the annual energy yield. So this is all about Solar Plant Performance | 987 | 4,436 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.03125 | 3 | CC-MAIN-2021-39 | latest | en | 0.930307 |
https://quizizz.com/en-us/mixed-numbers-and-improper-fractions-worksheets-grade-7 | 1,720,935,687,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514548.45/warc/CC-MAIN-20240714032952-20240714062952-00674.warc.gz | 416,193,534 | 26,027 | Mixed numbers and improper fractions
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31 Q
7th
## Explore printable Mixed Numbers and Improper Fractions worksheets for 7th Grade
Mixed Numbers and Improper Fractions worksheets for Grade 7 are essential tools for teachers to help their students master the concepts of fractions in mathematics. These worksheets provide a variety of exercises and problems that challenge students to convert between mixed numbers and improper fractions, simplify fractions, and perform operations with fractions. By incorporating these worksheets into their lesson plans, teachers can ensure that their Grade 7 students develop a strong foundation in understanding and working with fractions. Furthermore, these worksheets can be used for both in-class activities and homework assignments, allowing students to practice and reinforce their skills in a structured and engaging manner. Mixed Numbers and Improper Fractions worksheets for Grade 7 are an invaluable resource for teachers looking to enhance their students' mathematical abilities.
In addition to Mixed Numbers and Improper Fractions worksheets for Grade 7, Quizizz offers a wide range of resources for teachers to support their students' learning in math and other subjects. Quizizz is an online platform that allows teachers to create interactive quizzes, assignments, and activities that can be accessed by students on any device. With Quizizz, teachers can easily track their students' progress and identify areas where they may need additional support or practice. The platform also offers a vast library of pre-made quizzes and worksheets, covering topics such as fractions, decimals, algebra, geometry, and more, making it a one-stop-shop for all Grade 7 math resources. By incorporating Quizizz into their teaching strategies, teachers can provide a dynamic and engaging learning experience for their students, while also ensuring that they are well-prepared for success in their mathematical endeavors. | 773 | 3,311 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2024-30 | latest | en | 0.920093 |
https://www.askiitians.com/forums/Engineering-Entrance-Exams/the-velocity-of-sound-in-any-gas-depends-upon-a_84519.htm | 1,723,456,854,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641036895.73/warc/CC-MAIN-20240812092946-20240812122946-00386.warc.gz | 509,088,811 | 42,935 | # The velocity of sound in any gas depends upon (a) Wavelength of sound only (b) Density and elasticity of gas (c) Intensity of sound waves only (d) Amplitude and frequency of sound
Arun
25750 Points
4 years ago
Velocity of sound in any gas depends upon density and elasticity of gas.
Hence option B is correct.
Thanks and regards
Vikas TU
14149 Points
4 years ago
wave velocity= wavelength× frequency
hence wave velocity is directly proportional to wavelength
As wavelength increases, wave velocity also increases and vice versa. | 124 | 533 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2024-33 | latest | en | 0.797369 |
https://cooking.stackexchange.com/questions/104864/panna-cotta-gelatine-and-size-form | 1,726,238,935,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651523.40/warc/CC-MAIN-20240913133933-20240913163933-00072.warc.gz | 167,957,983 | 41,025 | # panna cotta gelatine and size/form
Suppose I've found my "sweet spot" for the amount of gelatine for a recipe of panna cotta which has been tried only for individual portions that are either turned upside down on a plate or topped and served directly in the glass.
If I were to make a bigger loaf to be sliced, how would I need to change the amount of gelatine? Would it be a good idea to increase it?
## 2 Answers
It depends.
• If your current “sweet spot” percentage gives you a panna cotta that’s sturdy enough to hold up on its own, so that you can make clean “cuts” with your spoon, you are fine also in larger shapes.
• If your preferred ratio is rather soft and creamy, so that the upside-down servings sag significantly, go up. Of course it won’t be as creamy and melty as before, you are making it more solid on purpose.
Only you know how your recipe turns out.
Yes. I would suggest you calculate the percent of gelatin that you use; that is, to the entire liquid mixture. Then, for a larger batch plug in your percentage and use that new amount.
• That's not what I was asking :) if my sweet spot for glass pannacotta is, say, 1% should I keep this 1%for a loaf or I increase it? Commented Jan 21, 2020 at 6:41
• Well, then, I think I answered your question anyway. Yes. If your sweet spot is 1% of 500 ml. then it would be 1% of 1000 ml. ...etc. Commented Jan 21, 2020 at 12:09
• Question was indeed whether the bigger the form the more gelatine makes sense to use for structure purposes Commented Jan 21, 2020 at 13:07
• I hear you. I am suggesting that the percentage of gelatin does not change (of course, the amount changes). Commented Jan 21, 2020 at 14:16 | 441 | 1,682 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2024-38 | latest | en | 0.964304 |
https://www.machinelearningplus.com/author/venmani/ | 1,721,509,504,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763517541.97/warc/CC-MAIN-20240720205244-20240720235244-00061.warc.gz | 750,929,530 | 95,950 | Drop a Query
# Venmani A D
## Bias Variance Tradeoff – Clearly Explained
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## Lambda Function in Python – How and When to use?
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## Python Yield – What does the yield keyword do?
Adding yield keyword to a function will make the function return a generator object that can be iterated upon. What does the yield keyword do? Approaches to overcome generator exhaustion How to materialize Generators? How yield works, step by step Exercise 1: Write a program to create a generator that generates cubes of numbers up …
## Matplotlib Subplots – How to create multiple plots in same figure in Python?
Subplots mean groups of axes that can exist in a single matplotlib figure. subplots() function in the matplotlib library, helps in creating multiple layouts of subplots. It provides control over all the individual plots that are created. Matplotlib Subplots in Python CONTENTS Basic Overview axes() function add_axis() function Creating multiple grids in the same graph …
## Matplotlib Line Plot – How to create a line plot to visualize the trend?
Line plot is a type of chart that displays information as a series of data points connected by straight line segments. A line plot is often the first plot of choice to visualize any time series data. Contents What is line plot? Simple Line Plot Multiple Line Plot in the same graph Creating a secondary …
## K-Means Clustering Algorithm from Scratch
K-Means Clustering is an unsupervised learning algorithm that aims to group the observations in a given dataset into clusters. The number of clusters is provided as an input. It forms the clusters by minimizing the sum of the distance of points from their respective cluster centroids. Contents Basic Overview Introduction to K-Means Clustering Steps Involved …
## Python Scatter Plot – How to visualize relationship between two numeric features
Scatter plot is a graph in which the values of two variables are plotted along two axes. It is a most basic type of plot that helps you visualize the relationship between two variables. Concept What is a Scatter plot? Basic Scatter plot in python Correlation with Scatter plot Changing the color of groups of …
## Requests in Python Tutorial – How to send HTTP requests in Python?
Requests is an elegant and simple Python library built to handle HTTP requests in python easily. It allows you make GET, POST, PUT and other types of requests and process the received response in a flexible Pythonic way. Contents Introduction to Requests Library What is a GET and POST request? GET Method Status Code Contents …
## Matplotlib Pyplot – How to import matplotlib in Python and create different plots
The pyplot object is the main workhorse of matplotlib library. It is through pyplot that you can create the figure canvas, various types of plots, modify and decorate them. Contents Pyplot: Basic Overview General Functions in pyplot Line plot Scatter plot Pie chart Histogram 2D Histograms Bar plot Stacked Barplot Boxplot Stackplot Time series plotting …
## Python Boxplot – How to create and interpret boxplots (also find outliers and summarize distributions)
Boxplot is a chart that is used to visualize how a given data (variable) is distributed using quartiles. It shows the minimum, maximum, median, first quartile and third quartile in the data set. What is a boxplot? Box plot is method to graphically show the spread of a numerical variable through quartiles. From the below …
## Bar Plot in Python – How to compare Groups visually
A bar plot shows catergorical data as rectangular bars with the height of bars proportional to the value they represent. It is often used to compare between values of different categories in the data. Content What is a barplot? Simple bar plot using matplotlib Horizontal barplot Changing color of a barplot Grouped and Stacked Barplots …
Course Preview | 903 | 4,534 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2024-30 | latest | en | 0.85661 |
https://socratic.org/questions/how-do-you-solve-21n-2-5n-6-0 | 1,701,791,812,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100551.2/warc/CC-MAIN-20231205140836-20231205170836-00356.warc.gz | 617,608,922 | 6,511 | # How do you solve 21n ^ { 2} + 5n - 6= 0?
Mar 28, 2018
$n = \frac{3}{7} , - \frac{2}{3}$
#### Explanation:
Given:
$\textcolor{w h i t e}{\times x} 21 {n}^{2} + 5 n - 6 = 0$
$\Rightarrow 21 {n}^{2} - 9 n + 14 n - 6 = 0$ [Broke up $5 n$ as $- 9 n + 14 n$]
$\Rightarrow 3 n \left(7 n - 3\right) + 2 \left(7 n - 3\right) = 0$ [Grouping the Like Terms]
$\Rightarrow \left(7 n - 3\right) \left(3 n + 2\right) = 0$ [Group Again]
Now, If :
$3 n + 2 = 0$, then $3 n = - 2 \Rightarrow n = - \frac{2}{3}$
And If :
$7 n - 3 = 0$, then $7 n = 3 \Rightarrow n = \frac{3}{7}$
Hence Explained.
Mar 28, 2018
$n = - \frac{2}{3} \text{ or } n = \frac{3}{7}$
#### Explanation:
$\text{factorise the quadratic using the a-c method}$
$\text{that is factors of "21xx-6=-126" which sum to } + 5$
$\text{the factors of "-126" which sum to + 5 are + 14 and - 9}$
$\textcolor{b l u e}{\text{split the middle term using these factors}}$
$\Rightarrow 21 {n}^{2} + 14 n - 9 n - 6 = 0 \leftarrow \textcolor{b l u e}{\text{factor by grouping}}$
$\Rightarrow \textcolor{red}{7 n} \left(3 n + 2\right) \textcolor{red}{- 3} \left(3 n + 2\right) = 0$
$\text{take out the common factor } \left(3 n + 2\right)$
$\Rightarrow \left(3 n + 2\right) \left(\textcolor{red}{7 n - 3}\right) = 0$
$\text{equate each factor to zero and solve for n}$
$3 n + 2 = 0 \Rightarrow n = - \frac{2}{3}$
$7 n - 3 = 0 \Rightarrow n = \frac{3}{7}$ | 601 | 1,413 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 23, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.78125 | 5 | CC-MAIN-2023-50 | latest | en | 0.50296 |
http://www.aaaknow.com/xlate/lessonFull.php?slug=multFacts1112B&menu=Multiplication | 1,550,874,108,000,000,000 | text/html | crawl-data/CC-MAIN-2019-09/segments/1550249406966.99/warc/CC-MAIN-20190222220601-20190223002601-00181.warc.gz | 298,834,115 | 6,284 | Multiplication Facts 11-12 Buttons
Multiplication: Learn
ELEVEN
11*0=0 11*1=11 11*2=22 11*3=33 11*4=44
11*5=55 11*6=66 11*7=77 11*8=88 11*9=99
11*10=110 11*11=121 11*12=132
TWELVE
12*0=0 12*1=12 12*2=24 12*3=36 12*4=48
12*5=60 12*6=72 12*7=84 12*8=96 12*9=108
12*10=120 12*11=132 12*12=144
Example: 4 * 6 = 24
The product of 24 is illustrated below
with 4 rows of 6 boxes or 6 columns of 4 boxes.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Multiplication: Practice
What is the product of the two numbers?
00:00
Press the Start Button To Begin
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This is 0 percent correct.
Play
Game Name Description Best Score
How many correct answers can you get in 60 seconds? 0
Extra time is awarded for each correct answer.
Play longer by getting more correct.
0
How fast can you get 20 more correct answers than wrong answers? 999 | 364 | 886 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.203125 | 3 | CC-MAIN-2019-09 | latest | en | 0.68061 |
https://www.geeksforgeeks.org/undecidability-and-reducibility-in-toc/?ref=leftbar-rightbar | 1,627,504,714,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046153791.41/warc/CC-MAIN-20210728185528-20210728215528-00394.warc.gz | 823,613,954 | 24,045 | Related Articles
# Undecidability and Reducibility in TOC
• Difficulty Level : Medium
• Last Updated : 28 Jun, 2021
Decidable Problems
A problem is decidable if we can construct a Turing machine which will halt in finite amount of time for every input and give answer as ‘yes’ or ‘no’. A decidable problem has an algorithm to determine the answer for a given input.
Examples
• Equivalence of two regular languages: Given two regular languages, there is an algorithm and Turing machine to decide whether two regular languages are equal or not.
• Finiteness of regular language: Given a regular language, there is an algorithm and Turing machine to decide whether regular language is finite or not.
• Emptiness of context free language: Given a context free language, there is an algorithm whether CFL is empty or not.
Undecidable Problems
A problem is undecidable if there is no Turing machine which will always halt in finite amount of time to give answer as ‘yes’ or ‘no’. An undecidable problem has no algorithm to determine the answer for a given input.
Examples
• Ambiguity of context-free languages: Given a context-free language, there is no Turing machine which will always halt in finite amount of time and give answer whether language is ambiguous or not.
• Equivalence of two context-free languages: Given two context-free languages, there is no Turing machine which will always halt in finite amount of time and give answer whether two context free languages are equal or not.
• Everything or completeness of CFG: Given a CFG and input alphabet, whether CFG will generate all possible strings of input alphabet (∑*)is undecidable.
• Regularity of CFL, CSL, REC and REC: Given a CFL, CSL, REC or REC, determining whether this language is regular is undecidable.
Note: Two popular undecidable problems are halting problem of TM and PCP (Post Correspondence Problem). Semi-decidable Problems
A semi-decidable problem is subset of undecidable problems for which Turing machine will always halt in finite amount of time for answer as ‘yes’ and may or may not halt for answer as ‘no’.
Relationship between semi-decidable and decidable problem has been shown in Figure 1 as:
Rice’s Theorem
Every non-trivial (answer is not known) problem on Recursive Enumerable languages is undecidable.e.g.; If a language is Recursive Enumerable, its complement will be recursive enumerable or not is undecidable.
Reducibility and Undecidability
Language A is reducible to language B (represented as A≤B) if there exists a function f which will convert strings in A to strings in B as:
`w ɛ A <=> f(w) ɛ B`
Theorem 1: If A≤B and B is decidable then A is also decidable.
Theorem 2: If A≤B and A is undecidable then B is also undecidable.
Question: Which of the following is/are undecidable?
1. G is a CFG. Is L(G)=ɸ?
2. G is a CFG. Is L(G)=∑*?
3. M is a Turing machine. Is L(M) regular?
4. A is a DFA and N is an NFA. Is L(A)=L(N)?
A. 3 only
B. 3 and 4 only
C. 1, 2 and 3 only
D. 2 and 3 only
Explanation:
• Option 1 is whether a CFG is empty or not, this problem is decidable.
• Option 2 is whether a CFG will generate all possible strings (everything or completeness of CFG), this problem is undecidable.
• Option 3 is whether language generated by TM is regular is undecidable.
• Option 4 is whether language generated by DFA and NFA are same is decidable. So option D is correct.
Question: Which of the following problems are decidable?
1. Does a given program ever produce an output?
2. If L is context free language then L’ is also context free?
3. If L is regular language then L’ is also regular?
4. If L is recursive language then L’ is also recursive?
A. 1,2,3,4
B. 1,2
C. 2,3,4
D. 3,4
Explanation:
• As regular and recursive languages are closed under complementation, option 3 and 4 are decidable problems.
• Context free languages are not closed under complementation, option 2 is undecidable.
• Option 1 is also undecidable as there is no TM to determine whether a given program will produce an output. So, option D is correct.
Question: Consider three decision problems P1, P2 and P3. It is known that P1 is decidable and P2 is undecidable. Which one of the following is TRUE?
A. P3 is undecidable if P2 is reducible to P3
B. P3 is decidable if P3 is reducible to P2’s complement
C. P3 is undecidable if P3 is reducible to P2
D. P3 is decidable if P1 is reducible to P3
Explanation:
• Option A says P2≤P3. According to theorem 2 discussed, if P2 is undecidable then P3 is undecidable. It is given that P2 is undecidable, so P3 will also be undecidable. So option (A) is correct.
• Option C says P3≤P2. According to theorem 2 discussed, if P3 is undecidable then P2 is undecidable. But it is not given in question about undecidability of P3. So option (C) is not correct.
• Option D says P1≤P3. According to theorem 1 discussed, if P3 is decidable then P1 is also decidable. But it is not given in question about decidability of P3. So option (D) is not correct.
• Option (B) says P3≤P2’. According to theorem 2 discussed, if P3 is undecidable then P2’ is undecidable. But it is not given in question about undecidability of P3. So option (B) is not correct.
Quiz on Undecidability | 1,366 | 5,217 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.546875 | 4 | CC-MAIN-2021-31 | latest | en | 0.875543 |
https://www.coursehero.com/file/8814691/Thus-pY-30-q1-q2-q3-q4-q5-At-the-other-extreme-Y-0/ | 1,487,581,951,000,000,000 | text/html | crawl-data/CC-MAIN-2017-09/segments/1487501170434.7/warc/CC-MAIN-20170219104610-00068-ip-10-171-10-108.ec2.internal.warc.gz | 814,610,919 | 21,583 | # Thus py 30 q1 q2 q3 q4 q5 at the other extreme y 0
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Unformatted text preview: nding the probability of failure of the upper branch by p1 + p2 and the lower branch by p3 + p4 and multiplying these bounds because the branches are independent. The numerical value is 0.000004 in case pi = 0.001 for 1 ≤ i ≤ 4. For network D, F = F1 F3 ∪ F2 F4 . The union bound for two events yields P (F ) ≤ p1 p3 + p2 p4 . The numerical value is 0.000002 in case pi = 0.001 for 1 ≤ i ≤ 4. Fo network E, F = F1 F3 ∪ F2 F4 ∪ F1 F5 F4 ∪ F3 F5 F2 . The union bound for four events yields P (F ) ≤ p1 p3 + p2 p4 + p1 p5 p4 + p3 p5 p2 . The numerical value is 0.000002002 in case pi = 0.001 for 1 ≤ i ≤ 5, which is approximately 0.000002. Note that for all four networks, B through E, the numerical value of the union bound, in case pi = 0.001 for all i, is close to the exact value of network outage computed above. Calculation by exhaustive listing of network states Another way to calculate the outage probability of an s − t network is to enumerate all the possible network states, determine which ones corre...
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## This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.
Ask a homework question - tutors are online | 422 | 1,451 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.296875 | 3 | CC-MAIN-2017-09 | longest | en | 0.8881 |
http://w3.pppl.gov/info/cl/List_Functions.html | 1,516,318,294,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084887660.30/warc/CC-MAIN-20180118230513-20180119010513-00776.warc.gz | 358,794,583 | 2,692 | Common Lisp Extensions. Node: List Functions
## 11.1: List Functions
This section describes a number of simple operations on lists, i.e., chains of cons cells.
This function is equivalent to `(car (cdr (cdr x)))`. Likewise, this package defines all 28 `cxxxr` functions where xxx is up to four ``a`'s and/or ``d`'s. All of these functions are `setf`-able, and calls to them are expanded inline by the byte-compiler for maximum efficiency.
Function: first x
This function is a synonym for `(car x)`. Likewise, the functions `second`, `third`, ..., through `tenth` return the given element of the list x.
Function: rest x
This function is a synonym for `(cdr x)`.
Function: endp x
Common Lisp defines this function to act like `null`, but signaling an error if `x` is neither a `nil` nor a cons cell. This package simply defines `endp` as a synonym for `null`.
Function: list-length x
This function returns the length of list x, exactly like `(length x)`, except that if x is a circular list (where the cdr-chain forms a loop rather than terminating with `nil`), this function returns `nil`. (The regular `length` function would get stuck if given a circular list.)
Function: last* x &optional n
This function returns the last cons, or the nth-to-last cons, of the list x. If n is omitted it defaults to 1. The ``last cons'' means the first cons cell of the list whose `cdr` is not another cons cell. (For normal lists, the `cdr` of the last cons will be `nil`.) This function returns `nil` if x is `nil` or shorter than n. Note that the last element of the list is `(car (last x))`.
The Emacs function `last` does the same thing except that it does not handle the optional argument n.
Function: butlast x &optional n
This function returns the list x with the last element, or the last n elements, removed. If n is greater than zero it makes a copy of the list so as not to damage the original list. In general, `(append (butlast x n) (last x n))` will return a list equal to x.
Function: nbutlast x &optional n
This is a version of `butlast` that works by destructively modifying the `cdr` of the appropriate element, rather than making a copy of the list.
Function: list* arg &rest others
This function constructs a list of its arguments. The final argument becomes the `cdr` of the last cell constructed. Thus, `(list* a b c)` is equivalent to `(cons a (cons b c))`, and `(list* a b nil)` is equivalent to `(list a b)`.
(Note that this function really is called `list*` in Common Lisp; it is not a name invented for this package like `member*` or `defun*`.)
Function: ldiff list sublist
If sublist is a sublist of list, i.e., is `eq` to one of the cons cells of list, then this function returns a copy of the part of list up to but not including sublist. For example, `(ldiff x (cddr x))` returns the first two elements of the list `x`. The result is a copy; the original list is not modified. If sublist is not a sublist of list, a copy of the entire list is returned.
Function: copy-list list
This function returns a copy of the list list. It copies dotted lists like `(1 2 . 3)` correctly.
Function: copy-tree x &optional vecp
This function returns a copy of the tree of cons cells x. Unlike `copy-sequence` (and its alias `copy-list`), which copies only along the `cdr` direction, this function copies (recursively) along both the `car` and the `cdr` directions. If x is not a cons cell, the function simply returns x unchanged. If the optional vecp argument is true, this function copies vectors (recursively) as well as cons cells.
Function: tree-equal x y `&key :test :test-not :key`
This function compares two trees of cons cells. If x and y are both cons cells, their `car`s and `cdr`s are compared recursively. If neither x nor y is a cons cell, they are compared by `eql`, or according to the specified test. The `:key` function, if specified, is applied to the elements of both trees. See Sequences.
Lists Lists Substitution of Expressions | 992 | 3,959 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2018-05 | latest | en | 0.789299 |
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We use different words to describe numbers depending on how many digits (numbers) they contain. We can also refer to the number of digits for simple generalisations. For example, 10,000 is five digits, so we refer to it as in the tens of thousands, but we may also call it a five figure number.
These are some of the ways we can describe numbers. Individual numbers will be called by their name, for instance 4 is four, 13,425 is thirteen thousand four hundred and 25. But they can also be grouped or generalised in a variety of ways. For instance 4 is also a single figure (or digit) number, and 13,425 is in the tens of thousands. The following table shows how we can describe some groups of numbers as they increase in size:
Name 13-19 teen 10 ten 100 hundred 1000 thousand 10,000 ten thousand 100,000 hundred thousand 1,000,000 million 1,000,000,000 billion 1,000,000,000,000 trillion
In the past, there was a distinction between the American billion (1,000,000,000) and the British or European billion (1,000,000,000,000 – now the trillion), but in modern use the vast majority of the English speaking world has adopted the American version.
# Saying a large number
We say large numbers by listing the numbers in order of size, biggest first. When reading a single number, all the number labels should be singular, for example 10,400 is ten thousand four hundred and not ten thousands four hundreds.
We describe three digit numbers in hundreds, then tens. Generally, in British English we usually connect large numbers with double or single digit figures with and, but in American English and is not used. Note that hundreds, thousands and millions are not connected to each other with and, though.
For example:
• 345 is three hundred and forty-five (three hundred forty five in American).
• 59,321 is fifty nine thousand, three hundred and twenty one. (not fifty nine thousand and three hundred…)
You can then describe large numbers with a series of different figures, grouping numbers in hundreds and tens, starting with the biggest number. So we describe hundreds/tens of millions, then thousands, then hundreds:
• 1,345,612 = one million, three hundred and forty five thousand, six hundred and twelve
• 153,200 = one hundred and fifty three thousand, two hundred
# In the…
When we want to say where a number generally lies, in the above groups, we can say it is in the… For example, 14 is in the teens, 325 is in the hundreds. For tens and hundreds of larger numbers (thousands, millions), we say in the tens (or hundreds) of… So: hundreds of thousands and tens of millions.
# Hundreds and thousands
Often it is easier to describe four figure numbers in hundreds instead of thousands. This is perfectly acceptable. For example, 1500 might be described as fifteen hundred, instead of one thousand five hundred (or one and a half thousand), because it is simpler to say.
# Numbers as adjectives
All of these numbers can be referred to by the number of figures they contain, with plurals, for instance a number is in single figures (3), double figures (20) or quadruple figures (1,000). However, when we use the figure size of the number to describe a noun (such as a salary, price or to refer to a number itself) we simply use number + figure + noun. For example, a six-figure salary, a four-figure discount.
# Alternative names for number groups
There are many informal alternative names for groups of numbers that can be used to simplify names. Beware you may not always be understood using these.
singular example plural 12 dozen 24 = 2 dozen 20 score 80 = 4 score 100 century 300 = centuries 1,000 grand, k
# Naming large numbers exercise
Practise reading these numbers out loud:
1. 4,567
2. 367
3. 98,745
4. 120,005
5. 5,000
6. 34,230
7. 873,120
8. 10,043
9. 7,340,200
10. 54,500
11. 24
12. 4,567,090
13. 67,000
14. 92,000,031
15. 1,000,010,000,023
1. 4,567 – four thousand, five hundred and sixty-seven
2. 342 – three hundred and forty-two
3. 98,745 – ninety-eight thousand, seven hundred and forty-five
4. 120,005 – one hundred and twenty thousand and five
5. 5,000 – five thousand, or five k, g or grand
6. 34,230 – thirty four thousand, two hundred and thirty
7. 873,120 – eight hundred and seventy three thousand, one hundred and twenty
8. 10,043 – ten thousand and forty three
9. 7,340,200 – seven million, three hundred and forty thousand, two hundred
10. 5,500 – five thousand, five hundred or fifty-five hundred
11. 24 – two dozen
12. 4,567,090 – four million, five hundred and sixty seven thousand and ninety
13. 67,000 – sixty seven thousand, sixty seven k, grand or g
14. 92,000,031 – ninety two million and thirty one
15. 1,000,010,000,023 – one trillion, ten million and twenty three
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# Data Representation / Numbering Conversion / File Permissions
### Main Objectives of this Practice Tutorial
• Understand how digital computers store data (i.e. data representation)
• Define decimal, binary, octal and hexadecimal numbers
• Manually perform numbering conversions between the decimal, binary, octal and hexadecimal numbering systems
(without the use of a computer or calculator)
• Identify which numbering system conversion method to use when required to perform a numbering conversion
• Explain the purpose of file permissions
• Explain how permissions work differently for directories as opposed to regular files.
• Change file permissions with the chmod command (both symbolic and absolute methods)
• Use the umask command to automatically assign permissions for directory and regular files to be created.
### Tutorial Reference Material
Course Notes Numbering Conversion / File Permissions Reference YouTube Videos Slides:PDF | PPTX Data Representation Definitions File Permission Concepts Introduction to File Permissions File Permission Commands Instructional Videos:
# KEY CONCEPTS
### Why Study Data Representation?
A series of binary numbers form a byte to represent numbers.(Image licensed under cc) Bytes can be used to also represent characters. It is job of a program to know if bytes are used to represent numbers or characters. Learning to convert numbering systems(like Hexadecimal to Binary) can be used to know how a character is represented in binary. (Image licensed under cc)
Data ... is any sequence of one or more symbols given meaning by specific act(s) of interpretation. Digital data is data that is represented using the binary number system of ones (1) and zeros (0)...
Reference: https://en.wikipedia.org/wiki/Data_(computing)
Binary numbers are combined in a sequence to form a byte. Bytes are used to represent numbers or characters. How does the computer know which bytes represent a number or a letter? That is the job of programs that are created (including operating systems and application software) to perform that task.
Examples of Understanding Data Representation:
• Network Specialists: Building Large Networks via Sub-netting
• C Programming: Sending information over networks, files
• Web Development: Setting color codes for webpage background or text
• Allowing or Limiting Unix / Linux File Access: Setting permissions for files and directories
### Decimal / Binary / Octal / Hexadecimal Numbering Systems
The decimal numbering system .
(Image licensed under cc - modified by author).
Decimal Numbers
The decimal numbering system consists of digits consisting of numbers 0 to 9. The numbering system is based on sums of the power of 10 which provides a framework for mathematic calculations.
The fact that humans started counting on their fingers and thumbs most likely lead to the development of this numbering system.
Referring to the diagram on the right, the value of each decimal digit consists of the value (placeholder) multiplied by the corresponding power of 10. For example, units are 100, tens are 101, hundred are 102 which move in a right-to-left direction.
The binary numbering system.
(Image licensed under cc)
Binary Numbers
The binary numbering system consists of digits containing the numbers 0 or 1. The numbering system is based on sums of the power of 2.
Digital computers have circuits which representing data in terms of voltage levels. Multiple circuits are used to represent data (in the form of binary numbers).
Referring to the diagram on the right, the value of each decimal digit consists of the value (placeholder) multiplied by the corresponding power of 2. For example, 20 , 21, 22, etc. which move in a right-to-left direction.
Octal / Hexadecimal Numbers
The octal numbering system.(Image licensed under cc) The hexadecimal numbering system.(Image licensed under cc)
The octal and hexadecimal numbering systems consist of digits containing numbers 0 to 7 and 0 to F respectively. For hexadecimal numbers, values for 10 to 15 are represented by the characters A to F respectively. The octal and hexadecimal numbering system are based on sums of the power of 8 and 16 respectively.
Since 1 octal digit represents 3 binary digits and 1 hexadecimal digit represents 4 binary digits, octal and hexadecimal numbers are used as short-cuts to represent binary number.
### Numbering Conversion Methods
#### Method 1: Binary to Decimal
Performing a binary to decimal conversion.
When converting binary numbers to decimal numbers, perform the following steps:
1. Write down the binary number.
2. Starting from the right-side, draw L's below the binary number moving to the left
(refer to diagram on right).
3. Starting on the rightmost "L", multiply the value (placeholder) by 2 to the power of zero.
4. Continually repeat step #3 moving leftwards, increasing the power of 2 by 1
(refer to diagram on right).
5. Add up the results to obtain the decimal value equivalent.
NOTE: To convert octal and hexadecimal numbers to decimal, replace the number 2
(in red in the diagram to the right) with 8 (for octal) or 16 (for hexadecimal).
#### Method 2: Decimal to Binary
Performing a decimal to binary conversion.
When converting decimal numbers to binary numbers, perform the following steps:
1. Write down the decimal number to be converted.
2. On the right-side, write the number 1 and moving leftwards, keep doubling the numbers until that number is greater than the decimal number to be converted (refer to the diagram on the right).
3. Starting on the right-side of those doubled numbers, compare that number with the decimal number. If that number if less than or equal to the decimal number, then write a 1 below and subtract that number from the decimal number to get a remainder. If the number is greater than decimal number (or remainder), then write a 0 below.
4. Repeat step #3 (moving leftwards and comparing the number with the decimal's remainder)
NOTE: If you are converting to 8-bit, 32-bit, etc., add leading zeros if necessary.
#### Method 3: Octal to Binary / Binary to Octal
Performing an binary to octal numbering conversion. Performing an octal to binary numbering conversion.
Binary to Octal
1. One octal number represents 3 binary numbers, so starting from right-side, group binary digits into groups of 3
(add leading zeros if necessary).
2. Write (4)(2)(1) under each group of 3 binary numbers.
3. Multiply the value or "placeholder" (i.e. 0's and 1's) by the corresponding (4)(2)(1) for each group to obtain the octal number (refer to diagram of binary to octal conversion).
Octal to Binary
1. One octal number represents 3 binary numbers, so space-out
the octal numbers to make space for a binary number.
2. Write (4)(2)(1) under each octal number.
3. Write 0's or 1's for each group of binary numbers to add up to the
corresponding octal number (refer to diagram of octal to binary conversion).
#### Method 4: Hexadecimal to Binary / Binary to Hexadecimal
Performing a binary to hexadecimal conversion. Performing a hexadecimal to binary conversion.
Binary to Hexadecimal
1. One hexadecimal number represents 4 binary numbers, so starting from right-side, group binary digits into groups of 4 (add leading zeros if necessary).
2. Write (8)(4)(2)(1) under each group of 4 binary numbers.
3. Multiply the values or "placeholders" (i.e. 0's and 1's) by the corresponding (8)(4)(2)(1) for each group to obtain the octal number.
4. Convert values from 10 to 15 to A to F
(refer to diagram of binary to hexadecimal conversion)
Hexadecimal to Binary
1. One hexadecimal number represents 4 binary numbers,
so space-out the hexadecimal numbers to make space for a binary number.
2. Convert letters A to F to 10 to 15 (refer to diagram of binary to hexadecimal conversion)
3. Write (8)(4)(2)(1) under each hexadecimal number.
4. Write 0's or 1's for each group of binary numbers to add up to the corresponding
hexadecimal number (refer to diagram of hexadecimal to binary conversion).
#### Method 5: Octal to Hexadecimal / Hexadecimal to Octal
For conversions between octal and hexadecimal numbers, use binary as a bridge.
To convert using the method, simply use binary as a "bridge".
Example:
To convert octal to hexadecimal, convert octal to binary, then convert binary to hexadecimal.
To convert hexadecimal to octal, convert hexadecimal to binary, then convert binary to octal.
### File Permissions
Since the Unix / Linux operating systems allow for multiple user accounts it is essential
to have a system to share or limit access to directories and files contained in those different user accounts.
Detailed directory listing showing permissions for a directory
and a regular file.
When directories and regular files are created, they are assigned to an owner
(typically the username which is the creator). To allow or limit access to those files and directories, those files and directories are assigned to an initial group referred to as a "primary group".
Users that own those directories and regular files are referred to as users, users that belong within the same group are referred to as same group members, and those users are do NOT belong to a particular group are referred to as other group members.
NOTE: In this course, we cannot create groups or assign users to groups - you may learn how to do
that if you take a Unix/Linux administration account. On the other hand, you can change which user,
existing same group members or existing other group members can or cannot access a directory or regular file.
Permissions of a directory that contain subdirectories and regular files. Permissions of a regular file contained within a directory.
File Permissions consist of two-layers:
First, the permissions of a directory that contains regular files, and second, permissions of the regular files themselves.
Permissions for Directory files have a different meaning than permissions for regular files:
• Referring to the left-most diagram above, read (r) permissions permit viewing directory contents, write (w) permissions allow subdirectories and regular files to be created in that directory, and execute (x) permissions permit access to that directory. These permissions relate to the 3 categories: user (owner), same group members, other group members.
• Referring to the rightmost diagram above, read (r) permissions permit viewing regular file contents, write (w) permissions allow file contents to be modified/edited, and execute (x) permissions permit the file to be run (e.g. running a program or shell script). Again, these permissions relate to the 3 categories: user (owner), same group members, other group members.
NOTE: The symbol dash "-" indicates that the permission is NOT granted.
The permissions of newly-created directories and regular files are automatically assigned via a user mask (we will discuss this shortly). In order to change permissions for directories and regular files, you would use the chmod command.
Changing File Permissions with 'chmod' command:
Symbolic Method:
The chmod can use symbols to add, remove, and set rwx permissions for user,
same group members, other group members or ALL categories:
CommandDescription
chmod ugo+x script.bashAdd execute permissions to the file script.bash so it can be run.
chmod u=rwx,go=x ~Set "pass-thru" permissions of your home directory for same group members and other group members to navigate to other subdirectories (that may have access / view permissions).
chmod go-w ~/sharedRemove write permissions for same group members and other group members for the directory ~/shared
chmod a=rx mySet read and execute permissions for the directory myfile.txt
Octal (Absolute) Method:
using octal numbers to represent setting file permissions.
You can use octal numbers to represent permissions.
Since 1 octal digit represents 3 binary digits, one octal digit can represent the rwx permission granted or NOT granted. The permissions rwz would be in the form of 3 binary digits (1 represents the permission granted and 0 represents the permission NOT granted.
NOTE: You can only use this method to set file permissions (as opposed to add or remove permissions).
CommandDescription
chmod 500 script.bashSet read and execute permissions for only the user for the file script.bash so it can be run.
chmod 711 ~Set "pass-thru" permissions of your home directory for same group members and other group members to navigate to other subdirectories (that may have access / view permissions).
chmod 750 ~/sharedSet full permissions for user, read and access permissions for some group members and no permissions for other group members for the directory ~/shared
chmod 555 myfile.txtSet read and execute permissions for the directory myfile.txt
NOTE: You can use the -R option to set permissions for directory, subdirectory and directory contents recursively.
Setting umask for newly-created directories. Setting umask for newly-created regular files
Setting Permissions for Newly-Created Directories and Regular Files (umask):
The umask command is used to set the permissions of newly-created directories and regular files.
Issuing the umask command without arguments will display the current umask value. Refer to the diagrams on the right-side to set the umask value for directories and regular files. Setting the umask value (for example umask 022) only takes effect for the current shell session unless the umask command is contained in a start-up file
(e.g. .profile, .bash_profile, or .bashrc).
# INVESTIGATION 1: NUMBERING CONVERSIONS
For this investigation, we will NOT be logged into our Matrix account, but it is recommended to have sheets of paper ready to manually perform numbering conversions.
NOTE: It is essential that you learn how to manually perform numbering conversions since you will NOT be permitted to perform quizzes, midterm, or your final exam with a computer or a calculator. Learning to quickly perform manual numbering conversions will may IT professional more productive such as setting permissions, designing computer networks, or selecting complex colors when developing webpages.
Only use a calculator to check your numbering conversion AFTER you have performed the operation manually.
You will now get practice performing numbering conversions.
Perform the Following Steps:
1. Let's convert the following 8-bit binary number 10111110 to a decimal number.
NOTE: It is important to learn and memorize the correct techniques to perform the
proper numbering conversion method (i.e. view the method above (drawing the L's).
2. Write the manual conversion on a sheet of paper.
3. Use a calculator to check your work. In MS Windows, you can set the calculator to Programming mode
by making the selection to binary, enter the binary number 10111110 and view the decimal equivalent.
Did you get the correct answer? If not, retry the method and check to see what you did wrong.
4. Perform a manual conversion of the decimal number 55 to an 8-bit binary number.
What method (displayed above) will you use? Use a calculator to check your work.
5. Perform a manual conversion of the octal number 461 to an 8-bit binary number.
What method (displayed above) will you use? Use a calculator to check your work.
6. Perform a manual conversion of the 8-bit binary number 11110001 to a hexadecimal number.
What method (displayed above) will you use? Use a calculator to check your work.
7. Perform a manual conversion of the hexadecimal number ABC to an 8-bit binary number.
What method (displayed above) will you use? Use a calculator to check your work.
8. Perform a manual conversion of the binary number 10101111 to an octal number.
What method (displayed above) will you use? Use a calculator to check your work.
9. Perform a manual conversion of the same binary number 10101111 to a hexadecimal number.
What method (displayed above) will you use? Use a calculator to check your work.
10. Perform a manual conversion of the octal number 5636 to a hexadecimal number.
What method (displayed above) will you use? Use a calculator to check your work.
11. Perform a manual conversion of the hexadecimal number D68 to an octal number.
What method (displayed above) will you use? Use a calculator to check your work.
12. When you have performed all of the numbering conversions above, then you can proceed to the next INVESTIGATION.
# INVESTIGATION 2: FILE PERMISSIONS
In this section, you will get experience using the chmod and umask commands
to set permissions for directories and files.
Perform the Following Steps:
1. Login your matrix account and issue a command to confirm you are located in your home directory.
2. Issue a single Linux command to create the following directory structure displayed in the diagram to the right.
3. Make certain that your current directory is your home directory.
NOTE: You will now run a shell script to confirm that you properly created that directory structure in your Matrix account.
4. Issue the following Linux command to run a checking script:
bash /home/murray.saul/scripts/week4-check-1
5. If you encounter errors and re-run the checking script until you receive a congratulations message, then you can proceed.
6. Issue Linux commands to create empty files for each of those newly created directories as show in diagram to the right:
NOTE: You will now run another shell script to confirm that you properly created those empty files within those specified directories.
7. Issue the following Linux command to run a checking script:
bash /home/murray.saul/scripts/week4-check-2
8. If you encounter errors and re-run the checking script until you receive a congratulations message, then continue the remaining steps.
Let's get practice understanding permissions, changing permissions, and setting your Linux account to automatically set permissions for newly created directories and regular files.
9. Issue the following Linux commands:
ls -ld ~/documents ~/clients ~/vendors
ls -lR ~/documents ~/clients ~/vendors
NOTE: You should see permissions already set for those newly created directories and regular files. What do these permissions mean for same group member and other group member access to those directory and regular files?
10. Let's limit access to the clients and vendors directories to only yourself and same group members. Issue the following Linux command:
chmod 750 ~/clients ~/vendors
11. Issue the ls command to confirm that the permissions for those directories have been changed.
NOTE: The -R option for the chmod command can change the file permissions recursively within a directory structure.
12. Issue the following Linux command: chmod 750 -R ~/documents
13. Again, use the ls command to confirm the permissions for the ~/documents, ~/document/memos , ~/documents/reports, and ~/documents/contracts directories.
14. Issue the following Linux command: ls -lR ~/documents
What do you noticed happened to the permissions for the regular files contained in those directories. Did those regular file permissions change?
We want to now change those regular file permissions to the following settings: r w - r - - - - -
15. Issue the following Linux commands:
chmod 740 ~/documents/memos/memo*.txt
chmod 740 ~/documents/reports/report*.txt
chmod 740 ~/dcouments/contracts/contract*.txt
16. Issue the ls -lR command for the ~/documents directory to confirm that those regular file permission have changed.
Let's get some practice setting permissions to allow users to make editing changes to regular files.
17. Issue the following Linux command: chmod ugo-w ~/documents/memos/memo*.txt
18. Use the ls command to verify that those regular file's permissions have changed.
19. Using the nano or vi text editor, open the regular file ~/documents/memos/memo1.txt, type in some text and try to save your editing changes.
What happened?
20. To abort your editing session in vi, type :q! and to abort your editing changes in nano, just type n when prompted to save editing changes
21. Issue the following Linux command to add write permissions for all files in the memos directory for yourself (i.e. user): chmod u+w ~/documents/memos/*
22. Repeat the previous step #19. What happened?
23. Issue the following Linux command to view permissions for your home directory: ls -ld ~
What does execute permissions mean for same group members and other group members in terms of your home directory?
24. Issue the following Linux command to create a new subdirectory: mkdir ~/shared
25. Issue the following Linux command: ls -l ~/shared
What are the permissions for this newly-created directory? Can other users access the directory pathname ~youruserid/shared ?
26. Issue the following Linux command (without an argument): umask
NOTE: You should see a four-digit octal number. Drop the leading zero on the left to obtain the default umask value.
27. Perform a mathematical calculation by taking the octal number 777 and subtracting the default umask value you determined in the previous step.
What is the result?
28. Convert that octal number result to a binary number. What does that represent as newly created directory permissions?
Does that correspond to the permissions for the newly created ~/shared directory?
29. Repeat steps #27 and #28 to see how a umask setting of 077 would affect permissions of newly-created directories.
30. Issue the following Linux command: umask 077
31. Issue the following Linux command (without arguments): umask
NOTE: You should notice the value 0077. By dropping the leading zero to the left, that would provide the default umask value of 077.
32. Issue the following Linux command: mkdir ~/shared2
33. Issue the following Linux command: ls -ld ~/shared2
Do the permissions for this newly created directory match the predicted permissions that you calculated in step #29?
34. Issue the following Linux command to create an empty regular file called myfile.txt in the ~/shared2 directory: touch ~/shared2/myfile.txt
35. Use the ls -l command to view the permissions for this newly created regular file.
What do you notice about those permissions?
36. Logout of your Matrix account, and then log-back into your Matrix account.
37. Issue the following Linux command (without arguments): umask
What happened? Referring to your notes, what do you need to do to make that umask value persistent?
38. After you complete the Review Questions sections to get additional practice, then work on your online assignment 2
and complete the sections 1 and 2 labelled: Practice Using The vi Text Editor and Permissions respectively.
# LINUX PRACTICE QUESTIONS
The purpose of this section is to obtain extra practice to help with your assignment #1, quizzes, your midterm, and your final ezam.
Here is a link to the MS Word Document of ALL of the questions displayed below but with extra room to answer on the document to simulate a quiz:
Your instructor may take-up these questions during class. It is up to the student to attend classes in order to obtain the answers to the following questions. Your instructor will NOT provide these answers in any other form (eg. e-mail, etc).
Review Questions:
1. List the number of digits for the following numbering systems:
• Decimal
• Binary
• Octal
• Hexadecimal
2. Write a simple chart to show which values are represented for letter A - F for a hexadecimal number.
3. How many binary digits does 1 octal digit represent?
4. How many binary digits does 1 hexadecimal digit represent?
5. Use manual numbering conversion to complete the table displayed to the right.
1. Write the chmod command (using the symbolic method) to set “pass-through” permissions
(eg. r w x - - x - - x) for your home directory using an absolute pathname.
Write a Linux command to verify that permissions where set.
2. Perform a binary to octal numbering conversion for the permissions: r w x - - x - - x
Write single Linux command to set “pass-through” permissions for your home directory,
using the absolute method (i.e. octal numbers).
3. Write a single Linux command to add read permissions for same group members for the ~/tests directory.
4. Write a single Linux command to remove write permissions for same group members
and other group members for the ~/projects directory. Use the symbolic method.
5. Write a single Linux command to set the permissions for the ~/assignments directory
to the following using the absolute method (i.e. octal numbers): r w x r - x - - x
Show your work to perform a binary to octal conversion.
Write the command below using octal numbers and using a relative-to-home pathname.
6. Assume that you just issued the command:
chmod u=rwx,go=x ~/linux/content
What would be the new permissions for the “content” directory?
7. Assume that you just issued the commands:
umask 077
mkdir mydir
touch mydir/myfile.txt
What would be the permissions for the newly created directory and regular file?
(show your work) | 5,266 | 25,148 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.4375 | 3 | CC-MAIN-2020-10 | latest | en | 0.827732 |
https://www.jiskha.com/archives/2009/02/19 | 1,596,993,849,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439738562.5/warc/CC-MAIN-20200809162458-20200809192458-00550.warc.gz | 717,397,459 | 21,263 | # Questions Asked onFebruary 19, 2009
1. ## math
ab+cd=34 ac+bd=38 ad+bc=43 what is a+b+c+d=? multiple choice: a)15 b)16 c)17 d)18 e)19 First, I tried guessing and testing, but couldn't find the correct answer. Then I tried isolating a a=(34-cd)/b I'm stuck, there are too many variables
2. ## chemistry
A current of 0.965 A is passed through 500 ml of 0.2 M solution of ZnSO4 for 10 min. The molarity of Zn2+ after deposition of Zn is 1. 0.1M 2. 0.5M 3. 0.8M 4. 0.194M
find out how long it takes a \$2700 investment to double if it is invested by 7% compounded semiannually. Round to the nearest tenth of a year . Use the formula A=P[1+r/n]^nt
4. ## math- need now
solve the equation by expressing each side as a power of the same base and then equating exponents 3125^x=1/square root 5
5. ## Math
What is half of 3/4?
6. ## spanish sra jmcguin
complete sentence with subjunctive of verb in parentheses. My answers are the ones with the astericks - Are they correct - thanks 1 No es verdad que Raul ( ser) ______ un mal excursionista ** sepa 2 Es probable que Titi y o ( ir) _______a caminar en el
7. ## Math
Assume that the set S has 10 elements. How many subsets of S have at most 4 elements? This question is from the section in my book called "Counting Partitions: Combinations." I would greatly appreciate any help! Thanks!
8. ## math
he said to his sister, he siad to his brother. What did the witty raindrop exclaim to all the others?
9. ## Calc help
find the area of the region enclosed by y=e^2x, y=e^5x, and x=1. i am having trouble seeing how this region looks like and having problems with how to start the problem in general. Much help is appreciated.
10. ## math
v = h(6 - (1/3)(2 - (2 h/5))^3 ) i try to solve this equation and i got (350+4h^2)/75 im not sure if this is correct please check it for me!
11. ## social studies
how people reduce air pollution in their city?
Is the SI unit of temperature celsius or kelvin? thanks
13. ## Chemistry
How do you determine the number of atoms in 28.7 grams of gold (Au)
14. ## Chemistry
C7H6O3(s) + C4H6O3(l) → C9H8O4(s) + HC2H3O2(l) is the equation. At 20 degree celsius, how many liters of acetic acid, HC2H3O2, would be formed? The density of acetic acid is 1.05g/cm3.
What is generalization? What words signal generalization and what words do not signal generalization?
16. ## algebra
Solve graphically. x-y=0 y=x² The reason I don't understand the question is the second equation with the x². How do I graph that? I'm not sure if I ever graphed with an exponent, and if I did, it was a long time ago. Thanks!
We are working on Fractions, mixed numbers and decimals. the problem says - write each decimal as a fraction or mixed number in simplest form... 0.7 or 0.08 ....ugg HELP
18. ## math
#1 If v=(6-(r^3/3))h and h/(2-r)=5/2 write V as a function of h . Simplify the function so that you can express it as a polynomial in h . #2 If y=ln(x) , write ln(x^x) as a simple function of y thxs alot!
19. ## Chemistry
What is the molecular formula of a molecule that has an empirical formula of CH2O and a molar mass of 120.12g/mol?
20. ## Math 116
On three consecutive passes, a football team gains 8 yards, lose 26 yards, and gain 16 yards. The total net yardage is how many yards. 8-26+16=32 yards. Is this right.
21. ## Algebra
Solve graphically. x-y=0 y=x² The reason I don't understand the question is the second equation with the x². How do I graph that? I'm not sure if I ever graphed with an exponent, and if I did, it was a long time ago. I'm reposting this because I didn't
22. ## sentence
somebody can help me to make sentence with this words? sat,sit,tub,top,stop,step Thank you for help!
23. ## Combinations
Assume that the set S has 10 elements. How many subsets of S have at most 4 elements? This question is from the section in my book called "Counting Partitions: Combinations." I would greatly appreciate any help! Thanks!
24. ## Pharmacy
I am in need of some help in being able to locate information for this assignment as it seems as though I am unable to locate the information for it. Select a culture with which you may or may not be familiar with. Trace its evolution into what is the
25. ## spelling
flower:rose::tree:??????
26. ## U.S.History
not sure Western farmers wanted "free silver" because they felt it would a. stabilize interests b. increase crop prices c. depress crop prices d. decrease the amount of money in circulation
27. ## U.S.History
What was a negative impact of "bonanza" farms? a. Output declined b. Farms got smaller c. Farms became disorganized d. oversupply led to lower prices D
28. ## Algebra
I have to write each of the following percent change into a ratio comparing it to the original quantity. Then I have to write it as a constant multiplier. This is the example in my book: 3% increase, 103/100, 1+0.03 So I understand how to do single digit
29. ## Chemistry
In a acid-base titration, 22.81 mL of an NaOH solution were required to neutralize 26.18 mL of a 0.1121 M HCl solution. What is the molarity of the NaOH solution?
30. ## Chemistry
A 0.2861 gram sample of an unknown acid (HX) required 32.63 mL of 0.1045 M NaOH for neutralization to a phenolphthalein endpoint. What is the molar mass of the acid?
31. ## U.S.History
i really need help with this question Describe the major territorial advances made by the United States in the 19th Century. any info will be helpful
32. ## English
Who does the monster care about in Mary Shelley's "Frankenstein"?
33. ## calculus
evaluate: integration of x^2 (square root of (1-2x^3))dx
34. ## Chemistry
What volume of 0.1209 M HCl is necessary to neutralize 0.5462 grams Ca(OH)2? Include a balanced chemical equation.
35. ## English
Would the real monster in Mary Shelley's Frankenstein be Victor Frankenstein because he just leaves the monster to care for himself and wants nothing to do with it? or someone else?
36. ## spelling
ocean:sea::river???
37. ## Physics
(1) A virtual image -7 cm tall and 17 cm away from a mirror is created by an object 7 cm away from a mirror. How tall is the object? What kind of mirror created the image? What is its focal length? (2) If a 1.75 m tall man is looking at a plane mirror from
Sorry, I didn't see this. Actually you have only one mixture; it happens to have two components. There is a more or less standard procedure for separating complete unknowns (that's where you know nothing about it) and if you know nothing about it that is
39. ## Law college level
Tragedy unfolded early this morning around 7:15 am as a local police officer failed to stop at a red light crashing into a crossing car wounding the officer but unfortunately killing a woman, and three children. Reports show that alcohol was not associated
41. ## Math
I need 3 ordered pairs of points that would be solutions to this equation. Can anyone help please, thanks! 4x - y = 7
42. ## Chemistry
If 150 mL of 1.73 M aqueous NaI and 235 g of Pb(NO3)2 are reacted stoichiometrically according to the balanced equation, how many grams of Pb(NO3)2 remain? Pb(NO3)2(aq) + 2NaI(aq) → PbI2(s) + 2NaNO3(aq) Molar Mass (g/mol) NaI 149.89 Pb(NO3)2 331.21
43. ## Math
identify fraction relationship of 5/10 of 20=
I need help really bad. What are the three ways that unbalanced forces can cause an object to change it's motion?
45. ## Maths - Trig
I just had a test, and one question I tried heaps of times and I still couldn't answer. It was "Prove secèsinè + cosecè cosè = 2cosecè " Can someone please tell me if proving this is possible at all? (But don't tell me how to solve it)
46. ## spelling
whirlwind:breeze::downpour:???
identify fraction relationships 5/10 of 20=
48. ## Spanish
Actividad 10 - ¿Y tú? Contesta las preguntas. (Answer the questions.) 1 ¿Qué clases tienes? ¿Son fáciles o difíciles? Yo tengo la clase de español y historia. Son fáciles. 2. ¿A qué hora tienes la clase de español? Yo tengo la clase de español
49. ## calculus i need help please
evaluate: integration of x^2 (square root of (1-2x^3))dx
50. ## Medical Terminology
devise memory aids for any five terms relating to the musculoskeletal system
51. ## Chemistry
I converted 789,032 calories to Kilo Joules, and I got 3,301,309,888. I feel like this number is way to big. I set up the proportion like this: 789,032 x 4.184J/1c x 1000 kj/1J. Was this incorrect?
52. ## spelling
glue:sticks::thorns:?????
53. ## To NEO LOUIS - Math
I've removed your very complicated post, for which you have supplied no thinking on your own. Please repost when you can demonstrate that you have tried to answer all these questions -- and/or when you ask specific questions about your assignment.
54. ## science
is solubility a chemical, or a physical property? Thanks
55. ## GCSE Biology
what is the process of carbon dioxide leaving leaves?
56. ## math
how far will the bike travel if the wheel makes 5 revolutions? the diameter is 40cm. show work
57. ## algebra-Needed Quick
find the domain of a logarithmic function of f(x)=log[2](x-9)
58. ## actuarial science
To get into an actuarial science program I was wondering was sort of high school courses I would need to take and what kind of marks I'd need to acheive. I`ve tried googling this but I can't seem to find information on this anywhere :S
60. ## Chemistry
What would be the molality of a solution made up of 75cm^3 of water and 0.21 g of NaCl?
61. ## math
solve: x lnx - 30 + 5 lnx - 6x = 0
62. ## science
Where in nature could you find a source of energy just like batteries
63. ## U.S.History
Which best describes the main goal of the social gospel and settlement movements a. to improve living conditions for the poor b. to strengthen political machines c. to encourage immigration d. to create jobs for the unemployed A
64. ## U.S.History
not so sure about this Most African American Exodusters migrated west to a. work as sharecroppers on bonanza farms b. escape racial violence in the South c. find relatives who had fled during the Civil War d. prospect for gold and silver
65. ## algebra
What percent of 320 is 220 my answer is 6.88 make as a decimal.is this right. -12(
66. ## college Econ
Suppose Fred and Ethel need to divide 20 pizza slices and 10 cans of beverage. Fred's utility function is given by the equation U=Min(Z,B), where Z is the amount of pizza and B is the amount of beverage. Ethel's utility is given by the equation
67. ## U.S.History
this is what i have. please add more. i'm adding detail by detail which is taking me very long, please just tell me the MAJOR territorial advances that i should add Describe the major territorial advances made by the United States in the 19th Century.
68. ## computer
unscramble this word ienerpgcd
70. ## math
a number between 1 and 100. If it is divided by 3 or 5, remainder is 1. If it is divided by 7, there is no remainder: what is my member?
71. ## english
when did bad behavior be considered the cool thing to do? is there like a history of bad behavior being the right thing to do to be accepted into society?
72. ## U.S.History
What was a negative impact of "bonanza" farms? a. output declined b. farms got smaller c. farms became disorganized d. oversupply led to lower prices i got D according to my book heres what my book says: The farms' massive output caused problems, however.
73. ## science
Is milk a homogenous mixture? Thanks-Elise
74. ## english
I'm having trouble understanding how to answer this question about a reading I did, the question is "could Joe have anticipated John's approach?" could anyone possibly help me understand what this question means better.....thanks
75. ## Chemistry
A 0.2861 gram sample of an unknow acid (HX) required 32.63 mL of 0.1045 m NAOH for neutralization to a thenolphthalein end point. what is the molar mass of the acid?
76. ## Math...Applying the Order of Operations
Can you please show me where i'm going wrong? Here's the question: 2(14+35/7) - ((-14 + -35)/-7) A.28 B.31 C.26 D.26 E.38 Here are the rules that apply: Multiplying and Dividing Integers. *If the signs are the same,then give the answer a positive sign. *If
77. ## Chemistry
What volume of 0.1209 M HCl is necessary to neutralize 0.5462 grams Ca(OH)2? Include a balanced chemical equation.
78. ## science
If the volume of 26.100 grams of chloroform has a density of 1.49 g per ml, then what is the mass? I got 18.125. Is this correct? My other question is, if the mass of an aspirin is 250 mg, then what is the mass in kg? I got, .00025. Is this correct?
79. ## Chemistry
I had to convert 95.4 km/hr to m/sec. Would this be the correct series of proportions? 95.4 km x .62m/1km x .60m/1hr x 60 sec/1 minute I then got 212932.8. If this is not correct, then what is the correct way? Thank you so much.
80. ## Physics
What is the difference between radiant, solar, and thermal energy? Thanks
what is lateral and total surface area? What does "B" stand for? What does "P" stand for? What does "H" stand for?
82. ## what number am i
i am a three digit number i am less than 200 i am divisible by 12 and by 9 my units digit is less than my tens digits
83. ## math
bayside insurance offers two health plans.Under plan A, Gisselle would have to pay the first 110 dollars of her, plus 25% of the rest. Under plan b, giselle would pay the first 230dollars , but only 20 % of the rest.for what amount of medical bills will
84. ## Science
Is it that the higher or lower the gradient, the steeper a distance is? Which one, higher or lower?
85. ## Chemistry
How do you determine the number of moles in 78.6 grams of carbon tetrachloride (CCl4) ?
86. ## science
Technetium is a transition metal similar to manganese. what chemical and physical properties would you expect technetium to have?
87. ## Civics
Can ayou Vote? Can you be elected? 1)You are a 43 year old Jewish merchant in Pennsylvania in 1705. can you be eleected to [rovincial counicle? Why or why not? 2) Yo are a 56 year old roman catholic farmer in new haven in 1646. Can you vote?
88. ## Language
Just a curious question. Which language would be more useful, Spanish or French.
89. ## chemistry
Dose the law of conservation work when doing an expirement with vinegar and baking soda.
90. ## Classroom Management
In the 6th grade social studeis class Mrs. Jones asked Tom to stop talking with his neighbor, but he continued. After three other reminders, Mrs Jones asked Tom to move to another seat. Tom refused saying "You can't make me move.: What would you do? Short
91. ## Geometry
What is the math equation to find the scaled version if 1"=2' for Bed dimentions 6'3"L X 3'2"W
92. ## Math 116
I post some question this morning why have no one help me
93. ## history
why, after 1765, did the American colonists increasingly find British imperial rule unacceptable? What had changed -- and why?
94. ## Financing
During the sixth month of the fiscal year, the program director of the Westchester Home-Delivered Meals (WHDM) program decides to again recompute fixed costs, variable costs, and the BEP using the high–low method. Here are the number of meals served and
95. ## accounting
The Mountain View Senior Adult Program (MVSAP) is interested in starting a visiting nurse program. The program would use licensed practical nurses to make home visits once a week to full-pay clients in the community. The MVSAP will treat the visiting nurse
96. ## Health
When were baked potato chips invented?
97. ## science
What is the difference between radiant, solar, and thermal energy? Thanks
98. ## Literature
what is an example of modern day hero? because my work asks me to compare modern heroes with Huck and Jim from Huck Finn. I need to tell if modern heroes will give up their lives and freedoms for friendship, loyalty and other important things...the answer
99. ## Science
If the volume of 26.100 grams of chloroform has a density of 1.49 g per ml, then what is the mass? I got 18.125. Is this correct? My other question is, if the mass of an aspirin is 250 mg, then what is the mass in kg? I got, .00025. Is this correct?
100. ## Math
You've got a bucket labeled Apples, and a bucket labeled Oranges, and a bucket labeled Apples and Oranges. You know they're all incorrectly labeled. How many pieces of fruit do you need to pull out, and from which buckets, before you can correct the
101. ## Western Civilization
I have a essay for Next Wednesday about The massacre on SAint Bartholomew's day. so i have to consider it again from perspective of four imaginary observers. One of them is Marcel, who is soldier in the royal army. then compose essay on how he is react or
In January, gasoline cost \$1.05 per gallon. In July, gasoline cost \$1.20 per gallon. Find the percent of increase. Would the answer for this question be 14.3? And how do you do percent of decrease? _______________________________________ The original cost
103. ## Math
Joe and Anna collect football cards.The greatest common factor of the numbers of cards in their collections is 15.Altogether Joe and Anna have 75 cards.If Joe has more cards than Anna,how many cards do they each have?
104. ## health
I have to make a 3D model of the urinary system for health class. I'm thinking clay might be best to use, but I'm not that artistic. Any other ideas??
106. ## Kodaly Beats
Hi i have found a nursery rhyme and sounded out the beat using Kodaly below. Hickory Dickory Dock The Mouse ran up the Clock The Clock Struck one The mouse ran down Hickory Dickory Dock The pattern of this song is as follows: Ti-ti ti-ti ti-ti ta Ti-ti
107. ## Algebra
Translate to a system of equations. DO NOT SOLVE. A nontoxic scouring powder is made up of 4 parts baking soda and 1 part vinegar. How much of each ingredient is needed for a 16-oz mixture? What are the two equations? For most problems, I can easily find
Can someone else explain it but more easier for an 8th grader ______________________________________ In January, gasoline cost \$1.05 per gallon. In July, gasoline cost \$1.20 per gallon. Find the percent of increase. Would the answer for this question be
109. ## Physical Science
what 2 substances found in my home that could conduct electricity and explain why?
110. ## math 116
6-2(3x-3) =-18 6-6x-6=-18 12x=-6=18=24 12x=24 x=2 check this problem is it right.
111. ## chemistry
which stage of ionization is likely favored?
112. ## chemistry
which stage of ionization is likely favored?
113. ## Song of Myself+English
Has anyone read Song of Myself by Walt Whitman?? I can't find any themes for it. So hard to understand. Would slavery be a theme? I need atleast 4 themes associated with Song of Myself.
114. ## Social Studies/American Government
Could you check my answers by the way they have to do with the Missouri State Missouri State Constitution. Missouri State Constitution. 1. What is the Preamble? Answer: The Preamble is the first paragraph of the Constitution, and it states why the
115. ## algebra
C leaves home going 40 km/h. when c is 9 km from home, d starts after c from the same place, going 58 km/h. how long does it take d to catch up to c?
116. ## U.S.History
A major failure or Reconstruction was that a. the South's cotton production never recovered b. war debts remained unpaid c. racist attitudes continued in the North and South d. no African Americans were voted into Congress any idea on this
117. ## Social Studies/Missouri Facts
Could you also check these thanks. Could I get a letter grade I'm in 9th grade 1. Who is the Governor of the State of Missouri? Answer: Jay Nixon 2. Name the two major cities in Missouri. Answer: St. Louis and Kansas City 3. Where is the capital of
118. ## math
what is the least common positive integer that meets the following conditions: divided by 7 with remainder 4 divided by 8 with remainder 5 divided by 9 with remainder 6 i thought you could add 7 and 4 to get 13, then divide 13 and 7 with r=4, but it has to
119. ## math
x lnx - 30 + 5 lnx - 6x = 0
What were Caesar's reasons for attacking Gaul? (Be Specific) What was his "Campaign against the Helvetti" and what did he do during his years in Gaul?
121. ## college
Ethernet or Token Ring
122. ## algebra
7/d=14/d^ help with this problem 3(5-8)-3-1-2-6)= help with this problem
123. ## algebra
find f^-1(x) f(x)=x-5
124. ## U.S.History
i cant find this in my book. i've probably read about it but i don't remember In the 1890s, immigration patters shifted dramatically, with most immigrants now coming from a. northern European countries b. southern and eastern European countries c. Mexico
125. ## Algebra I
Write each percent change as a ratio comparing the result to the original quantity. Then write it as a constant multiplier. Book's example: 3% increase, 103/100, 1+0.03 I don't understand double digit numbers. The one that I have to solve is an 11%
126. ## U.S.History
The Pendleton Civil Act was passed to a. place additional regulation on the railroads b. end Japanese immigration to the U.S. c. end the spoils system d. print money backed by silver rather than gold C
127. ## Chemistry
I am supposed to add up these numbers, using the significant digits rules. 150 76.9 209 .036 I got 435.936. Following the sig. digs. rules, it would be 435.9, right? How does this then equal 440 as my science books says? Thank you so much.
128. ## Algebra
Were doing factoring and i don't get these (^ means squared) 1) m^-3m-2 2) 6c^-5c-4 3) ab+mn+an+mb 4) The length of a rectangular garden is 5ft more than the width. The garden has a 3ft wide cement walk sorrounding it. The total area of the garden and the
129. ## Algebra cont
d^=7d-12 (factoring the same as the last one
130. ## Math
Determine whether the function is one-to-one. If it is, find itd inverse. f(x)= 3x+4 over 5
given f(x) = abs(sin x) and g(x) = x^2 for all real x: 1) let H(x) = g(f(x)) and write an expression for it. 2) find domain and range of H(x). 3) find an equation of the line tangent to the graph of H at the point where x = pi/4.
132. ## Math 116
42/-6=-7 check these problem 3(c-5)= 3c-15= c= 3/15 C=5 Check this answer for me. Find decimal notation for the fraction -1/17. The decimal notation for the-1/17 is round to the nearest hundreth i get 589
133. ## Chemistry
What is the STP for 2.84g of (NH3)2(SO4)
134. ## chemistry
what is the volume at standard temperature and pressure for 28.4g of N2H6SO3?
135. ## U.S.History
please check these are some questions from the opening lines of Gettysburg Address. a. when Lincoln referred to "four score and seven years ago" what year was he talking about? 1776 b. What did Lincoln say the Civil War was testing? whether our nation can
136. ## chemistry acids and bases
which solution is potentially more hazardous to your eyes: .1M HCl or .1M NaOH? Why? are they equally hazardous since one is an extremely strong acid and one is an extremely strong base?
137. ## U.S.History
Prohibitions and purity crusaders shared the goal of a. making charity "scientific" b. redistributing the nation's wealth c. ending immigration from Asia d. improving the personal behavior of individuals i'm not 100% sure but i think D
138. ## spanish sra jmcguin
complete sentences with indicative or subjunctive forms of verb in parentheses 1. (ser) No dudi que Juan _____la mejor persona pra hacer el trabejo. **sea 2. ( tener) El conductir no niega que _____poca experencia por estas calles **tenga 3. ( decir )
139. ## Languages
How do you say, Happy Valentines Day in Spanish and in French?
140. ## U.S.History
someone answered this a while back, i just want to know if its correct What happened at the Massacre at Wounded Knee? a. American soldiers killed more than 200 unarmed Sioux b. General Custer's cavalry was completetly wiped out c. the Nez Perce fought for
141. ## Accounting
The Ritz Manor is a popular seaside resort. A double room costs \$220 for one night. In order to reserve a room, guests must pay one night’s stay in advance. On each floor of the hotel, Vendalite Company operates vending machines with energy bars, juices,
142. ## math
hi, could someone please help me solve this problem, i know the answer is 24, i just need to know how to solve it. a "lucky dollar" is one of nine symbols on each reel of a slot machine with three reels. a player receives one of the various payouts
143. ## History
In granting or gaining of civil rights to or by many groups in America, what were the 3 most important? Why were they the most important?
144. ## Chemistry
Determine the percent composition by mass of ammonia sulfate.
Do all poems need to rhyme? If so, give me the examples> Thanks.
146. ## algebra
how to simplify these expressions using positives exponents to express the final result 6-3= 5XO= (2x)-1=
147. ## Chemistry+balancing equation tips
We are on combustion reaction at the moment in chemistry, and I have to say, these reactions are like extremely hard to balance(well, just alot of erasing). It takes me a while to balance combustion reactions and I want to know if theres any tips in
148. ## Algebra
Find the decimal notaiton for the fraction -1/17, the decimal notation for the -1/17 is 0.5889 round it the hundreth.
149. ## science
how does a food web start? | 6,716 | 25,301 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.171875 | 3 | CC-MAIN-2020-34 | latest | en | 0.88491 |
https://calculate.org.au/2019/05/20/thelanguageofmaths/ | 1,720,929,602,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514548.45/warc/CC-MAIN-20240714032952-20240714062952-00849.warc.gz | 132,799,311 | 24,421 | ## The Language of Mathematics
##### The following allow us to reflect on the language we use in Mathematics and how we can support students in their learning of concepts by using the correct terminology.
Recently, I was working with a school on their NAPLAN analysis. As we worked through the Item Analysis Report it became clear to the leaders of the school that some of the language and vocabulary presented in NAPLAN created confusion for many students across the school. As a result of these insights, a Professional Learning session was planned for all staff, addressing correct and consistent use of Mathematical Language, in order to ensure that students are exposed to the correct terminology.
The process used for this session began by identifying the purpose of the Professional Learning session. Firstly, every staff member was asked to record the words they currently use when teaching the four operations and lists were created from these. ‘Plus’, ‘add’ and ‘make’, were some of the words used for addition. Lists were also created for Subtraction, Multiplication and Division.
Mathematical vocabulary taken from the Australian Curriculum relating to the four operations were then added to the lists. Many of these had not been identified as part of current vocabulary being used.
Partitioning, for example, is sometimes referred to as number busting or breaking numbers. If different words are used to describe the same concept, students may experience confusion and be unable to access the Mathematics concept of partitioning as consistent language is not being used.
The word ‘sum’ is yet another example. It is often used when describing a number sentence or an equation, however this is an incorrect use of the word as it refers to the total in an addition problem. In this case, the terms ‘number sentence’ and ‘equation’ would be better options to use. Unfortunately, many commercially produced materials do refer to number sentences and equations as sums. Unfortunate but true!!!
In pairs, teachers were provided with the overview of the Australian Curriculum. The task was to highlight the Mathematical terminology which existed. This exercise allowed teachers to focus on the vocabulary which exists in the Mathematics curriculum and provided an opportunity to reflect on their current use of Mathematical language. At the completion of the task a couple of questions were posed:
Some questions to consider:
• Are we exposing students to the mathematical vocabulary in the Australian Curriculum?
• Are we providing students with the opportunity to access the mathematics through the language?
• Is the mathematical vocabulary being used consistent across the school?
These questions allow us to reflect on the language we use in mathematics and can show how we can support students in their learning of concepts by using the correct terminology.
The Power Point included outlines the process used in one CHOOSEMATHS school but it can be adapted in address your own school context.
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Permutation vs. combination vs arrangement
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Permutation vs. combination vs arrangement [#permalink]
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23 Jan 2009, 15:45
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can someone please give me an example repeated with slight changes that would illustrate the following?
1-a case when arrangement is used
2- a case when permutation is used
3- a case when combination is used.
I'm just having trouble understand when to use either when i read a problem and it's really confusing.
Thanks
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Re: Permutation vs. combination vs arrangement [#permalink]
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27 Jan 2009, 10:27
can someone please give me an example repeated with slight changes that would illustrate the following?
1-a case when arrangement is used
2- a case when permutation is used
3- a case when combination is used.
I'm just having trouble understand when to use either when i read a problem and it's really confusing.
Thanks
Permutation means arrangement of things. The word arrangement is used, if the order of things is considered.
so 1 and 2 are same:)
Combination means selection of things. The word selection is used, when the order of things has no importance.
Suppose we have to form a number consisting of three digits using the digits 1,2,3,4, To form this number the digits have to be arranged. Different numbers will get formed depending upon the order in which we arrange the digits. This is an example of Permutation.
Now suppose that we have to make a team of 11 players out of 20 players, This is an example of combination, because the order of players in the team will not result in a change in the team. No matter in which order we list out the players the team will remain the same! For a different team to be formed at least one player will have to be changed.
hope it is clear now
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Permutation vs. combination vs arrangement [#permalink]
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23 Jun 2015, 19:29
pecas wrote:
can someone please give me an example repeated with slight changes that would illustrate the following?
1-a case when arrangement is used
2- a case when permutation is used
3- a case when combination is used.
I'm just having trouble understand when to use either when i read a problem and it's really confusing.
Thanks
Bumping this up because the first answer wasn't satisfactory, and I was studying it myself...
-Combination is the selection of a group from a number of items, or people. There is a group which is selected and a group not selected, and so the formula nCr has the number selected and number unselected dividing the total number. Order is without significance.
$$\frac{n!}{r!(n-r)!}$$
-Permutation is the arragement of a group from a number of items, or people. There is a group which is selected AND ordered, and the formula nPr has the number of unselected dividing the total number. The order of the items, or people, selected are what concerns us, and therefore the unselected is cleared out.
$$\frac{n!}{(n-r)!}$$
Tip:
-If you are working from selection and the solution is required without order, divide by the number of which are not to be ordered. That said, the reverse is true too; if you are working from an ordered solution, multiply by number of items selected to unarrage them.
-Slot method is a way of setting up a problem, and it is used for both combination and permutations, selections and arrangements, respectively.
-Arragement is what the problem is asking for, but permutation is the standard formula to solve it.
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Re: Permutation vs. combination vs arrangement [#permalink]
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23 Jun 2015, 22:16
Expert's post
mejia401 wrote:
-Slot method is a way of setting up a problem, and it is used for both combination and permutations, selections and arrangements, respectively.
Note here that slot method by default arranges. You are choosing for particular slots so you have numbered the positions. That is arrangement. If it is pure selection, you will have to un-arrange the result.
Check this post:
http://www.veritasprep.com/blog/2011/11 ... binations/
The basic counting principle is the same as slot method.
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Re: Permutation vs. combination vs arrangement [#permalink]
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24 Jun 2015, 12:29
VeritasPrepKarishma wrote:
mejia401 wrote:
-Slot method is a way of setting up a problem, and it is used for both combination and permutations, selections and arrangements, respectively.
Note here that slot method by default arranges. You are choosing for particular slots so you have numbered the positions. That is arrangement. If it is pure selection, you will have to un-arrange the result.
Check this post:
http://www.veritasprep.com/blog/2011/11 ... binations/
The basic counting principle is the same as slot method.
Good point, Thanks Karishma. They are all so closely related that it's awfully easy to get tied up in them and trip. Slot method, or the basic counting principle, is an arrangement first before anything else.
Re: Permutation vs. combination vs arrangement [#permalink] 24 Jun 2015, 12:29
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Display posts from previous: Sort by | 1,665 | 6,750 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.0625 | 4 | CC-MAIN-2016-22 | latest | en | 0.907366 |
https://exercism.io/tracks/common-lisp/exercises/roman-numerals/solutions/cdd423e7bcee463891ccd15119d5ef58 | 1,590,385,217,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347387219.0/warc/CC-MAIN-20200525032636-20200525062636-00190.warc.gz | 339,585,738 | 7,667 | ## to Roman Numerals in the Common Lisp Track
Published at Feb 20 2020 · 0 comments
Instructions
Test suite
Solution
Write a function to convert from normal numbers to Roman Numerals.
The Romans were a clever bunch. They conquered most of Europe and ruled it for hundreds of years. They invented concrete and straight roads and even bikinis. One thing they never discovered though was the number zero. This made writing and dating extensive histories of their exploits slightly more challenging, but the system of numbers they came up with is still in use today. For example the BBC uses Roman numerals to date their programmes.
The Romans wrote numbers using letters - I, V, X, L, C, D, M. (notice these letters have lots of straight lines and are hence easy to hack into stone tablets).
`````` 1 => I
10 => X
7 => VII
``````
There is no need to be able to convert numbers larger than about 3000. (The Romans themselves didn't tend to go any higher)
Wikipedia says: Modern Roman numerals ... are written by expressing each digit separately starting with the left most digit and skipping any digit with a value of zero.
To see this in practice, consider the example of 1990.
In Roman numerals 1990 is MCMXC:
1000=M 900=CM 90=XC
2008 is written as MMVIII:
2000=MM 8=VIII
## Setup
Check out Installing Common Lisp for instructions to get started or take a look at the guides available in the track's side bar.
## Formatting
While Common Lisp doesn't care about indentation and layout of code, nor whether you use spaces or tabs, this is an important consideration for submissions to exercism.io. Excercism.io's code widget cannot handle mixing of tab and space characters well so using only spaces is recommended to make the code more readable to the human reviewers. Please review your editors settings on how to accomplish this. Below are instructions for popular editors for Common Lisp.
### VIM
Use the following commands to ensure VIM uses only spaces for indentation:
``````:set tabstop=2
:set shiftwidth=2
:set expandtab
``````
(or as a oneliner `:set tabstop=2 shiftwidth=2 expandtab`). This can be added to your `~/.vimrc` file to use it all the time.
### Emacs
Emacs is very well suited for editing Common Lisp and has many powerful add-on packages available. The only thing that one needs to do with a stock emacs to make it work well with exercism.io is to evaluate the following code:
`(setq-default indent-tabs-mode nil)`
This can be placed in your `~/.emacs` (or `~/.emacs.d/init.el`) in order to have it set whenever Emacs is launched.
One suggested add-on for Emacs and Common Lisp is SLIME which offers tight integration with the REPL; making iterative coding and testing very easy.
## Source
The Roman Numeral Kata http://codingdojo.org/cgi-bin/index.pl?KataRomanNumerals
## Submitting Incomplete Solutions
It's possible to submit an incomplete solution so you can see how others have completed the exercise.
### roman-numerals-test.lisp
``````(ql:quickload "lisp-unit")
(defpackage #:roman-test
(:use #:cl #:lisp-unit))
(in-package #:roman-test)
(define-test test-1
(assert-equal "I" (roman:romanize 1)))
(define-test test-2
(assert-equal "II" (roman:romanize 2)))
(define-test test-3
(assert-equal "III" (roman:romanize 3)))
(define-test test-4
(assert-equal "IV" (roman:romanize 4)))
(define-test test-5
(assert-equal "V" (roman:romanize 5)))
(define-test test-6
(assert-equal "VI" (roman:romanize 6)))
(define-test test-9
(assert-equal "IX" (roman:romanize 9)))
(define-test test-27
(assert-equal "XXVII" (roman:romanize 27)))
(define-test test-48
(assert-equal "XLVIII" (roman:romanize 48)))
(define-test test-59
(assert-equal "LIX" (roman:romanize 59)))
(define-test test-93
(assert-equal "XCIII" (roman:romanize 93)))
(define-test test-141
(assert-equal "CXLI" (roman:romanize 141)))
(define-test test-163
(assert-equal "CLXIII" (roman:romanize 163)))
(define-test test-402
(assert-equal "CDII" (roman:romanize 402)))
(define-test test-575
(assert-equal "DLXXV" (roman:romanize 575)))
(define-test test-911
(assert-equal "CMXI" (roman:romanize 911)))
(define-test test-1024
(assert-equal "MXXIV" (roman:romanize 1024)))
(define-test test-3000
(assert-equal "MMM" (roman:romanize 3000)))
#-xlisp-test
(let ((*print-errors* t)
(*print-failures* t))
(run-tests :all :roman-test))``````
``````(defpackage #:roman
(:use #:cl)
(:export #:romanize))
(in-package #:roman)
(defun romanize (number)
(labels ((split-number (number)
(if (zerop number)
nil
(cons (mod number 10) (split-number (truncate (/ number 10))))))
(convert-to-roman (value)
(cond
((zerop value) nil)
((<= value 3) (make-string value :initial-element #\i))
((= value 4) "iv")
((= value 5) "v")
((= value 9) "ix")
(t (concatenate 'string "v" (make-string (- value 5) :initial-element #\i)))))
(substitute (char substitutions 0) #\i
(substitute (char substitutions 1) #\v
(substitute (char substitutions 2) #\x roman-number)))))
(let* ((partially-converted (map 'list #'convert-to-roman (split-number number)))
partially-converted '("IVX" "XLC" "CDM" "M ")))
(cleaned (remove-if #'null fully-converted)))
(apply #'concatenate 'string (reverse cleaned)))))`````` | 1,389 | 5,202 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.0625 | 3 | CC-MAIN-2020-24 | latest | en | 0.911661 |
https://tastingbritain.co.uk/how-do-you-test-a-coil-with-a-multimeter/ | 1,719,028,529,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862249.29/warc/CC-MAIN-20240622014659-20240622044659-00520.warc.gz | 496,112,486 | 26,256 | # How do you test a coil with a multimeter?
Ignition coils have two circuits that require checking; primary and secondary circuits. Connect the multimeter to the negative and positive terminals of the ignition coil to get a primary circuit reading. If the multimeter shows a reading of 0 ohms, the ignition coil has shorted and needs replacing.
## How many volts should a magneto produce?
The voltage generated by a magneto is 50 volts. The coil increases this to 15,000 volts.
How do you test a coil with a multimeter? – Related Questions
## What causes magnetos to fail?
The Capacitor
Capacitors, which are short-term storage devices, often fail in older magnetos due to dielectric degradation (short circuit) or conductor breakage (open circuit). A short circuit absorbs all the power, hence no output or spark.
## How many volts should a coil be putting out?
The coil becomes a transformer, stepping the voltage up. If your car uses a 12 volt battery, the 12 volts you put into the primary side of the coil will exit the secondary side as 30,000 volts!
## How do you check voltage on a magneto?
Take off the rubber casing, set your multimeter to Ohms (Ω), and make sure the Ohm range is set to 40k without any auto-ranging. Place the multimeter probes at the magneto copper winding and the metal clip under the rubber casing. Any value below or above the 3k to 15k range implies that the magneto coil is faulty.
## How many volts should be at coil?
The voltage reaching the coil may be 12 volts , or about 7 volts if the coil has a ballast resistor . Most electrical equipment works on 12 volts, but most modern cars have a resistor in the ignition system to assist starting. The coil in a ballast-resistor system is rated at 7-8 volts instead of 12 volts.
## How many ohms is a good ignition coil?
Most ignition coils should have a primary resistance falling somewhere between 0.4 and 2 ohms; however, refer to your manufacturer’s specifications for the correct reading. If a reading of zero is displayed, that signifies that the ignition coil has shorted internally in the primary windings and needs to be replaced.
## How many ohms should a ignition coil read?
The ohmic resistance of the coil is around 0.2–3.0 Ω on the primary side and around 5–20 kΩ on the secondary side. The winding ratio of primary to secondary winding is 1:100. The technical structure may vary depending on the ignition coil’s area of application.
## How many amps does a 12v ignition coil draw?
To illustrate, an oil-filled ignition coil might require about 4 amperes of current at 12 volts to produce 20-30 kilovolts (kV), while a modern e-core or coil-on-plug configuration might require about 7 amperes of current at 12 volts to produce 30-60 kV of high-intensity spark.
## How many ohms should a 12-volt coil have?
You should have a resistance reading of at least 3-4.5 ohms. A bad coil will show a higher reading then 3-4.5. Next, place the red or black lead from the meter to the centre of the coil , and to either one of the terminals positive or negative. You want 9500-10000 Ohms, a little less is ok but no more.
## How many ohms should a 12-volt battery have?
The resistance “seen” by the 12-Volt battery is 500 ohms .
## What voltage is too high for a 12-volt battery?
If your battery has a charge between 12.4V and 12.7V, your battery is fully charged and ready to run. If your voltage is below 12.2V, it needs to be recharged. Take a 30-minute drive on the highway or pick up a charger to bring the voltage back up. If your voltage is higher than 12.9V, the battery is overcharged.
## What should a 12-volt battery read at rest?
When the probes touch the terminals while the car is off and the battery is resting, the multimeter display should show a reading of 12.2 to 12.6 volts (full charge). This voltage range means the battery is in good condition for starting the vehicle. | 939 | 3,903 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2024-26 | latest | en | 0.927375 |
http://www.intmath.com/methods-integration/9-integration-tables.php | 1,455,345,865,000,000,000 | text/html | crawl-data/CC-MAIN-2016-07/segments/1454701166222.10/warc/CC-MAIN-20160205193926-00189-ip-10-236-182-209.ec2.internal.warc.gz | 477,157,333 | 39,752 | # 9. Integration Using Tables of Integrals
by M. Bourne
### Leibniz's original integral notation
Gottfried Leibniz's original notation for integrals included an overbar, similar to what we use with square roots today. [Image source]
A lot of the integrals in this section can easily be done using a Table of Integrals. (Of course, use a computer to do integrals whenever you can!)
Points to note:
• It's very important to understand the substitutions u and du (which is the case for most integrations)
• Make sure you use the correct formula!! Some are very similar to others.
• Even if you are supplied with a table of integrals in examinations, learn as many as you can, and especially learn the conditions that apply. Too many students try to find the right one in the table, but have no idea what they are doing!
### Example using Table of Integrals
Find the following integral, using table of integrals:
inte^(2x)\ sin\ 3x\ dx
There are some more examples of using the Table of Integrals in the section, Integration by Reduction Formulae.
### Online Algebra Solver
This algebra solver can solve a wide range of math problems. (Please be patient while it loads.)
### Calculus Lessons on DVD
Easy to understand calculus lessons on DVD. See samples before you commit. | 289 | 1,283 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2016-07 | longest | en | 0.888689 |
https://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/900/2/a/b/ | 1,716,388,852,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058557.6/warc/CC-MAIN-20240522132433-20240522162433-00875.warc.gz | 747,470,321 | 57,866 | # Properties
Label 900.2.a.b Level $900$ Weight $2$ Character orbit 900.a Self dual yes Analytic conductor $7.187$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$
# Related objects
Show commands: Magma / PariGP / SageMath
## Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,2,Mod(1,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: $$N$$ $$=$$ $$900 = 2^{2} \cdot 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 900.a (trivial)
## Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: yes Analytic conductor: $$7.18653618192$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 20) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$
## $q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
$$f(q)$$ $$=$$ $$q - 2 q^{7}+O(q^{10})$$ q - 2 * q^7 $$q - 2 q^{7} - 2 q^{13} - 6 q^{17} - 4 q^{19} + 6 q^{23} - 6 q^{29} - 4 q^{31} - 2 q^{37} - 6 q^{41} + 10 q^{43} - 6 q^{47} - 3 q^{49} - 6 q^{53} - 12 q^{59} + 2 q^{61} - 2 q^{67} + 12 q^{71} - 2 q^{73} + 8 q^{79} + 6 q^{83} + 6 q^{89} + 4 q^{91} - 2 q^{97}+O(q^{100})$$ q - 2 * q^7 - 2 * q^13 - 6 * q^17 - 4 * q^19 + 6 * q^23 - 6 * q^29 - 4 * q^31 - 2 * q^37 - 6 * q^41 + 10 * q^43 - 6 * q^47 - 3 * q^49 - 6 * q^53 - 12 * q^59 + 2 * q^61 - 2 * q^67 + 12 * q^71 - 2 * q^73 + 8 * q^79 + 6 * q^83 + 6 * q^89 + 4 * q^91 - 2 * q^97
## Embeddings
For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below.
For more information on an embedded modular form you can click on its label.
comment: embeddings in the coefficient field
gp: mfembed(f)
Label $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
1.1
0
0 0 0 0 0 −2.00000 0 0 0
$$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles
## Atkin-Lehner signs
$$p$$ Sign
$$2$$ $$-1$$
$$3$$ $$-1$$
$$5$$ $$1$$
## Inner twists
This newform does not admit any (nontrivial) inner twists.
## Twists
By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 900.2.a.b 1
3.b odd 2 1 100.2.a.a 1
4.b odd 2 1 3600.2.a.be 1
5.b even 2 1 180.2.a.a 1
5.c odd 4 2 900.2.d.c 2
12.b even 2 1 400.2.a.c 1
15.d odd 2 1 20.2.a.a 1
15.e even 4 2 100.2.c.a 2
20.d odd 2 1 720.2.a.h 1
20.e even 4 2 3600.2.f.j 2
21.c even 2 1 4900.2.a.e 1
24.f even 2 1 1600.2.a.w 1
24.h odd 2 1 1600.2.a.c 1
35.c odd 2 1 8820.2.a.g 1
40.e odd 2 1 2880.2.a.f 1
40.f even 2 1 2880.2.a.m 1
45.h odd 6 2 1620.2.i.h 2
45.j even 6 2 1620.2.i.b 2
60.h even 2 1 80.2.a.b 1
60.l odd 4 2 400.2.c.b 2
105.g even 2 1 980.2.a.h 1
105.k odd 4 2 4900.2.e.f 2
105.o odd 6 2 980.2.i.i 2
105.p even 6 2 980.2.i.c 2
120.i odd 2 1 320.2.a.f 1
120.m even 2 1 320.2.a.a 1
120.q odd 4 2 1600.2.c.e 2
120.w even 4 2 1600.2.c.d 2
165.d even 2 1 2420.2.a.a 1
195.e odd 2 1 3380.2.a.c 1
195.n even 4 2 3380.2.f.b 2
240.t even 4 2 1280.2.d.g 2
240.bm odd 4 2 1280.2.d.c 2
255.h odd 2 1 5780.2.a.f 1
255.i odd 4 2 5780.2.c.a 2
285.b even 2 1 7220.2.a.f 1
420.o odd 2 1 3920.2.a.h 1
660.g odd 2 1 9680.2.a.ba 1
By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
20.2.a.a 1 15.d odd 2 1
80.2.a.b 1 60.h even 2 1
100.2.a.a 1 3.b odd 2 1
100.2.c.a 2 15.e even 4 2
180.2.a.a 1 5.b even 2 1
320.2.a.a 1 120.m even 2 1
320.2.a.f 1 120.i odd 2 1
400.2.a.c 1 12.b even 2 1
400.2.c.b 2 60.l odd 4 2
720.2.a.h 1 20.d odd 2 1
900.2.a.b 1 1.a even 1 1 trivial
900.2.d.c 2 5.c odd 4 2
980.2.a.h 1 105.g even 2 1
980.2.i.c 2 105.p even 6 2
980.2.i.i 2 105.o odd 6 2
1280.2.d.c 2 240.bm odd 4 2
1280.2.d.g 2 240.t even 4 2
1600.2.a.c 1 24.h odd 2 1
1600.2.a.w 1 24.f even 2 1
1600.2.c.d 2 120.w even 4 2
1600.2.c.e 2 120.q odd 4 2
1620.2.i.b 2 45.j even 6 2
1620.2.i.h 2 45.h odd 6 2
2420.2.a.a 1 165.d even 2 1
2880.2.a.f 1 40.e odd 2 1
2880.2.a.m 1 40.f even 2 1
3380.2.a.c 1 195.e odd 2 1
3380.2.f.b 2 195.n even 4 2
3600.2.a.be 1 4.b odd 2 1
3600.2.f.j 2 20.e even 4 2
3920.2.a.h 1 420.o odd 2 1
4900.2.a.e 1 21.c even 2 1
4900.2.e.f 2 105.k odd 4 2
5780.2.a.f 1 255.h odd 2 1
5780.2.c.a 2 255.i odd 4 2
7220.2.a.f 1 285.b even 2 1
8820.2.a.g 1 35.c odd 2 1
9680.2.a.ba 1 660.g odd 2 1
## Hecke kernels
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(900))$$:
$$T_{7} + 2$$ T7 + 2 $$T_{11}$$ T11
## Hecke characteristic polynomials
$p$ $F_p(T)$
$2$ $$T$$
$3$ $$T$$
$5$ $$T$$
$7$ $$T + 2$$
$11$ $$T$$
$13$ $$T + 2$$
$17$ $$T + 6$$
$19$ $$T + 4$$
$23$ $$T - 6$$
$29$ $$T + 6$$
$31$ $$T + 4$$
$37$ $$T + 2$$
$41$ $$T + 6$$
$43$ $$T - 10$$
$47$ $$T + 6$$
$53$ $$T + 6$$
$59$ $$T + 12$$
$61$ $$T - 2$$
$67$ $$T + 2$$
$71$ $$T - 12$$
$73$ $$T + 2$$
$79$ $$T - 8$$
$83$ $$T - 6$$
$89$ $$T - 6$$
$97$ $$T + 2$$ | 2,730 | 5,536 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2024-22 | latest | en | 0.404441 |
https://the-equivalent.com/what-is-equivalent-to-3-2/ | 1,679,665,059,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296945282.33/warc/CC-MAIN-20230324113500-20230324143500-00486.warc.gz | 653,306,152 | 12,987 | # What is equivalent to 3/2
## What is the fraction 3 2 equal to?
1 ½Answer: The value of 3 divided by 2 as a fraction is 3/2 = 1 ½.
## What is the ratio 2/3 equivalent to?
Answer: 4/6, 6/9, 8/12, 10/15 … are equivalent to 2/3. All those fractions obtained by multiplying both the numerator and denominator of 2/3 by the same number are equivalent to 2/3.
## What fraction is equivalent to?
Equivalent Fractions ChartUnit FractionEquivalent Fractions1/32/6, 3/9, 4/12..1/42/8, 3/12, 4/16..1/52/10, 3/15, 4/20,..1/62/12, 3/18, 4/24,..4 more rows
## What is 2/3 of a whole?
2/3, when converted to decimals, will be equal to 0.66 which is when rounded off to the nearest whole number will be equal to 1 because the value after the decimal is greater than 5, so it will be rounded up to the nearest whole number. Hence, 2/3 as a whole number will be 1.
## What is 2/3 as a percent?
We can see that this gives us the exact same answer as the first method: 2/3 as a percentage is 66.67%.
## What is the fraction 3/4 equivalent to?
Equivalent fractions of 3/4 : 6/8 , 9/12 , 12/16 , 15/
## What is 1/3 the same as?
Answer: The fractions equivalent to 1/3 are 2/6, 3/9, 4/12, etc. Equivalent fractions have the same value in the reduced form. Explanation: Equivalent fractions can be written by multiplying or dividing both the numerator and the denominator by the same number.
## What is 3/5 equivalent to as a fraction?
So, 3/5 = 6/10 = 9/15 = 12/20.
## How do you find the equivalent ratio?
Thus, to find a ratio equivalent to another we have to multiply the two quantities, by the same number. Another way to find equivalent ratios is to convert the given ratio into fraction form and then multiply the numerator and denominator by the same number to get equivalent fractions.
## How do you calculate a ratio?
Ratios compare two numbers, usually by dividing them. If you are comparing one data point (A) to another data point (B), your formula would be A/B. This means you are dividing information A by information B. For example, if A is five and B is 10, your ratio will be 5/10.
## What are equivalent ratios 6th grade?
Equivalent ratios have the same value. To determine whether two ratios are equivalent, write them as fractions. If the fractions are equal, the ratios are equivalent.
## How do you find three equivalent ratios?
0:518:14How to Find Equivalent Ratios – YouTubeYouTubeStart of suggested clipEnd of suggested clipSo 24 to 36 is equivalent it holds the same value as the ratio 8 to 12 now I can multiply both ofMoreSo 24 to 36 is equivalent it holds the same value as the ratio 8 to 12 now I can multiply both of them by 10 and get 80 to 120 as long as I do the same thing to both numbers of that ratio.
## How to find equivalent fractions?
To find equivalent fractions, you just need to multiply the numerator and denominator of that reduced fraction ( 23) by the same natural number, ie, multiply by 2, 3, 4, 5, 6
## Is 2 3 a fraction?
Important: 2 3 looks like a fraction, but it is actually an improper fraction.
## Can you convert fractions to decimals?
This Equivalent Fractions Table/Chart contains common practical fractions. You can easily convert from fraction to decimal, as well as, from fractions of inches to millimeters.
## What is the equivalent of 2 6?
The fraction 2 6 is equal to 1 3 when reduced to lowest terms. To find equivalent fractions, you just need to multiply the numerator and denominator of that reduced fraction ( 1 3) by the same integer number, ie, multiply by 2, 3, 4, 5, 6 … and so on …
## How to find equivalent fractions?
To find equivalent fractions, you just need to multiply the numerator and denominator of that reduced fraction ( 13) by the same natural number, ie, multiply by 2, 3, 4, 5, 6
## Is 1 3 a fraction?
Important: 1 3 looks like a fraction, but it is actually an improper fraction.
## Can you convert fractions to decimals?
This Equivalent Fractions Table/Chart contains common practical fractions. You can easily convert from fraction to decimal, as well as, from fractions of inches to millimeters.
## What is the equivalent of (3+7)+2?
The expression equivalent to (3+7)+2 is 12.
## What is the equivalent fraction of 2/3?
For example, if we multiply the numerator and denominator of 2/3 by 4 we get. 2/3 = 2×4 / 3×4 = 8/12 which is an equivalent fraction of 2/3.
## What is equivalent expression calculator?
Equivalent Expression Calculator is a free online tool that displays the equivalent expressions for the given algebraic expression. BYJU’S online equivalent expression calculator tool makes the calculations and simplification faster and it displays the equivalent expression in a fraction of seconds.
## Is 3y+3 true?
True, because when the numbers are in the parethasis that means you multiply what is outside of the parenthasis like the three by the numbers inside of the parenthasis so 3 x y and 3 x 1, therefore 3y+3 and 3 (y+1) is true.
## Is 3y+3 a simplified expression?
The expressions 3y+3 and 3 (y+1) are equivalent expressions. Because 3 (y+1) can be simplified as 3y+3. | 1,363 | 5,109 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5 | 4 | CC-MAIN-2023-14 | latest | en | 0.911107 |
https://www.blogarama.com/search-posts/?search=polynomial | 1,656,409,693,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103360935.27/warc/CC-MAIN-20220628081102-20220628111102-00394.warc.gz | 738,795,267 | 11,265 | ## Number Of Real Roots Of A Quintic Polynomial – Math.stackexchange.com
Online Web Tricks · 13:10 01 Feb 2018
Obtain the number of real roots of the following quintic polynomial $$f(x)= x^5+x^3-2x+1$$ My approach: First, on seeing the polynomial, it should be clear that it is continuous. Also, ...fr… Read More
## Division Of One Polynomial By Another. – Math.stackexchange.com
Online Web Tricks · 12:40 02 Feb 2018
How is this done? For example, how would one simplify this: $$\frac{x^3-12x^2+0x-42}{x^2-2x+1}$$ I can do it with long division, but it never makes intuitive sense to me. Either an explanati… Read More
## How To Show That The Following Function Isn't A Polynomial Over Q? – Mathoverflow.net
Online Web Tricks · 20:51 11 Dec 2017
Enumerate the rationals as $b_1,b_2,\dots$ and define the (set) function: $$f(x) = (x-b_1)^2 + (x-b_1)^2(x-b_2)^2 + \dots.$$ At any particular $x$, only finitely many terms are non zero so t… Read More
## Why Can’t You Use Cyclotomic Polynomials To Factor Big Numbers Really Quickly? – Mathoverflow.net
Online Web Tricks · 02:36 13 Feb 2018
Two simple remarks: The polynomial $x^k-1$ can be factorised over the integers as a product of (irreducible) cyclotomic polynomials: $$x^k-1 = \prod_{d|k}\Phi_d(x).$$ If we choose $k$ to be… Read More
0 | 398 | 1,297 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.359375 | 3 | CC-MAIN-2022-27 | latest | en | 0.735368 |
http://financial-dictionary.thefreedictionary.com/Efficient+Portfolios | 1,477,622,206,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988721555.36/warc/CC-MAIN-20161020183841-00381-ip-10-171-6-4.ec2.internal.warc.gz | 101,467,122 | 12,778 | # Markowitz efficient portfolio
(redirected from Efficient Portfolios)
## Markowitz efficient portfolio
Also called a mean-variance efficient portfolio, a portfolio that has the highest expected return at a given level of risk.
## Markowitz Efficient Portfolio
In Markowitz Portfolio Theory, a portfolio with the highest level of return at a given level of risk. One who carries such a portfolio cannot further diversify to increase the expected rate of return without accepting a greater amount of risk. Likewise one cannot decrease his/her exposure to risk without proportionately decreasing the expected return. A Markowitz efficient portfolio is determined mathematically and plotted on a chart with risk as the x-axis and expected return as the y-axis. See also: Markowitz efficient set of portfolios, Homogeneous expectations assumption.
References in periodicals archive ?
The firm offers a comprehensive suite of single-asset and multi-asset solutions designed to serve as powerful building blocks for smarter, more efficient portfolios.
In order to estimate the diversification benefits of Shariah non-compliant listed construction companies and Shariah-compliant listed construction companies in a mixed asset portfolio, efficient portfolios and optimal asset allocations are constructed applying data generated from Solver using the risk, returns and correlation data calculated from DataStream over 20 years (1993-2013).
Secondly, to select the optimal portfolio from the set of efficient portfolios, Capital Allocation Line (CAL) is drawn.
We show how to compute the semiparametric upper and lower bounds for MV+CVaR efficient portfolios and then perform the bound analysis on those portfolios.
According to modern portfolio theory, recognizing the relationship among asset classes is essential for constructing efficient portfolios.
The main conclusions of the research by the EDHEC-Risk Institute are that, first, a cap-weighted stock market index is not the market portfolio of financial theory (the Capital Asset Pricing Model (CAPM) theory is often evoked to show that cap-weighted stock market indices are efficient portfolios and attractive investments).
Sharpe advanced the asset allocation process by creating a multidimensional framework in attempting to create efficient portfolios.
We also have a series of specialist teams - for charities; tax efficient portfolios for inheritance tax, income tax and capital gains tax relief; and providing investment services for entrepreneurs.
Impact Investing, headquartered in Sydney, Australia, is a software development company specializing in analytical software tools for equity portfolio managers to aid them in their day to day role of managing money - making investment decisions, constructing efficient portfolios and communicating their conclusions and results.
He also offers a framework for understanding the interdependence between financial policies, analyses and forecasts in creating efficient portfolios and enhancing stockholder wealth.
In summary, that is why they are interesting tools for investors to use when constructing highly efficient portfolios.
Site: Follow: Share:
Open / Close | 560 | 3,176 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.625 | 3 | CC-MAIN-2016-44 | longest | en | 0.870844 |
https://socratic.org/questions/what-is-pi-10-in-degrees | 1,685,716,324,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224648695.4/warc/CC-MAIN-20230602140602-20230602170602-00422.warc.gz | 586,460,778 | 5,595 | # What is ((pi)/10) in degrees?
Jun 26, 2018
$\frac{\pi}{10} \text{ radians } = {18}^{\circ}$
#### Explanation:
Use how:
$2 \pi \text{ radians } = {360}^{\circ}$
$\implies \pi \text{ radians } = {180}^{\circ}$
$\implies \frac{\pi}{10} \text{ radians} = {18}^{\circ}$ | 107 | 273 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 4, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4 | 4 | CC-MAIN-2023-23 | latest | en | 0.591763 |
http://stackoverflow.com/questions/2290522/reordering-list-of-jquery-objects-to-columns | 1,435,880,228,000,000,000 | text/html | crawl-data/CC-MAIN-2015-27/segments/1435375095677.90/warc/CC-MAIN-20150627031815-00230-ip-10-179-60-89.ec2.internal.warc.gz | 249,013,724 | 17,655 | # Reordering list of jQuery objects to columns
I'm working on function, that takes a `select` from html and replaces it with multi-column `ul` - it's one list, but has `float:left;` on `li` children, so the number of columns is based on calculations (if `ul` width is 600 and `li` width is 200, i will obviously have 3 columns).
That's theory - the easy part.
Example: 5 items, 2 columns
Now, When I take data from select, I have this list:
`````` 1
2
3
4
5
``````
If I just push the array into `ul`, it will look like this on screen:
``````1 2
3 4
5
``````
But for user/reader, it's easier and better, when you don't read `Left->Bottom`, but rather `Bottom->Left`, meaning that you're reading until bottom of column and then move to next column, rather than reading row, then next row.
So I need to transform list to columns:
``````1 4
2 5
3
``````
so, in reality in `ul` will be this order:
``````1 4 2 5 3
``````
And this needs to work with variable column number, because if we decide to add 10 items to list, it might look better with more columns.
Any help with needed operators/cycles and math involved?
Thank you
-
I thought this was an interesting problem, so I wrote you a plugin for this. I tested it a little and it seems to work. Let me know if this is what you want!
http://jsbin.com/ocama/3/edit
http://jsbin.com/ocama/3
The algorithm is pretty simple, it pretty much just comes down to finding how many rows there are and grouping columns based on that number.
-
that's very nice :] – Adam Kiss Feb 18 '10 at 18:20
If you know how many columns there are, then you would make your `<li>` elements by skipping through the list n at a time. So for three columns, you pick items 0, 3, 6, ... and then come back and pick 1, 4, 7 and then 2, 5, 8.
-
kind of what I was thinking as well. another might be to create multiple lists and put them side by side...same thought process just put first x in column 1, next x+ and so forth. – Mark Schultheiss Feb 18 '10 at 17:40
I tell how many there are... I was just kind of lost how to pick 0,3,6 and all that math. solved now :] – Adam Kiss Feb 18 '10 at 18:26
I did all the calulation. I also like Alex's solution, so I'll give him good answer and I add my solution here just for anyone looking for this kind of problem :)
``````var rows= 2; //editable number of rows
\$('body').append('<ul id="fromselect"></ul>');
var o = \$('select#tolist option');
var ul = \$('ul#fromselect');
var total = o.size();
var onecol = Math.ceil(total / rows);
var index = 0; //index in o list
for (var j=1; j<=onecol;j++){
for (var i=1;i<=rows;i++){
if (!(i*j>total)){ //in last row, there might be less columns used
index = (i-1)*onecol+j-1;
ul.append('<li><a href="#">'+index +': '+
o.eq(index ).text()
+'</a></li>');
//index is used more for debug, you can put
//the index calculation in o.eq( * ) part
}
}
}
``````
- | 847 | 2,904 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.765625 | 3 | CC-MAIN-2015-27 | latest | en | 0.942981 |
https://greatgreenwedding.com/what-is-the-phenotypic-ratio-pr-of-the-offspring/ | 1,696,149,876,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510810.46/warc/CC-MAIN-20231001073649-20231001103649-00706.warc.gz | 315,236,394 | 9,982 | ## What is the phenotypic ratio Pr of the offspring?
The phenotypic ratio is the distribution pattern (expressed as a ratio) of the physical characteristics in the offspring obtained after a genetic cross. So, genotypic ratio and phenotypic ratio are the two types of genetic ratios used to express the genotype and the phenotype of offspring from a genetic cross.
## Is P generation dominant or recessive?
This P generation was a true breeding one, in that they only had a pure genotype for whatever phenotype Mendel was looking at. Once crossed, these plants would always produce the dominant phenotype, but their genotype would feature both dominant and recessive genes.
How do you calculate Punnett Squares?
Count the total number of boxes in your Punnett Square. This gives you the total number of predicted offspring. Divide the (number of occurrences of the phenotype) by (the total number of offspring). Multiply the number from step 4 by 100 to get your percent.
### How do you find the phenotypic ratio of an offspring?
Divide each frequency by the smallest one, and note the answer in the margins of the table. For example, if there are 10 in category one and 30 in category two, 10 divided by 10 equals 1 and 30 divided by 10 equals 3. Write the phenotypic ratio using rounding when appropriate.
### What is P genetics?
p in population genetics: The frequency of the more common of two different alternative (allelic) versions of a gene. (The frequency of less common allele is q).
What generation is P generation?
Parental generation
Parental generation is the first generation involving two individuals that are mated to foresee or analyze the genotypes of their offspring. Their probable set of offspring would constitute the so-called first filial generation (or F1 generation).
## How do you find the genotype ratio?
To find the genotypic ratio, count the number of times each combination appears in the grid, starting in the upper left square. The example in Figure 1 below is crossing alleles for just one trait, flower color. Larger Punnett squares are used to calculate genotypic ratios for more than one trait as shown in Figure 2.
## How is the Punnett square used in genetics?
J. Phelan, in Encyclopedia of Genetics, 2001. The Punnett square itself is a table in which all of the possible genetic outcomes for a given mating are listed. In its simplest form, the Punnett square consists of a square divided into four quadrants. Across the top of the table, all possible genotypes for the haploid female gamete are listed.
How did Gregor Mendel use a Punnett square?
Gregor Mendel demonstrated by crossing pea plants with different characteristics that gametes combine randomly. He used a Punnett square to predict the outcome of any genetic cross.
### How is the Punnett square divided into four quadrants?
In its simplest form, the Punnett square consists of a square divided into four quadrants. All possible genotypes for the haploid female gametes are listed across the top, one genotype at the head of each column; and down the left side of the square, all of the possible genotypes for the haploid male gametes are listed, one per row.
### What was the result of Annett’s Punnett square?
Referring to the Punnett square and the assumption that all alleles are uniformly distributed, Annett was able to charge the proportion of handedness. The result of the model is almost equal with the actual distribution. This theory influenced Geschwind and Galaburda (1985a, 1985b, 1985c) in their research. | 759 | 3,547 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.421875 | 3 | CC-MAIN-2023-40 | longest | en | 0.93267 |
https://getrevising.co.uk/revision-cards/finding-the-nth-term-sequences | 1,527,122,208,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794865863.76/warc/CC-MAIN-20180523235059-20180524015059-00208.warc.gz | 552,536,615 | 13,253 | # Finding the Nth Term - Sequences
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## Finding the Nth Term
Term:- 0 1 2 3 4 5
3, 7, 11, 15, 19
Write an expression in terms of n for the above number sequence.
• Find the number rule +4
• Find the zero (0) term for the above sequence -1
• Write the nth term 4n - 1
• Check it 4n - 1 4 x1(1st term) -1 = 3 which is the 1st term
Answer:- 4n - 1
rule +4 zero term -1
1 of 2
## Finding the Nth Term
Term:- 0 1 2 3 4 5
30, 24, 18, 12, 6
Write an expression in terms of n for the above number sequence.
• Find the number rule -6
• Find the zero (0) term for the above sequence 36
• Write the nth term -6n + 36
• Check it -6n + 36 -6 x1(1st term) +36 = 30 which is the 1st term
Answer:- -6n + 36
rule -6 zero term 36
2 of 2
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# What is the maximum and minimum magnitude of 2i+3j and 5i-2j
Dhruv
28 Points
3 years ago
Add them to get maximum magnitude. (2i+3j) + (5i-2j) = 7i+j
Hence maximum magnitude = square root of (72 + 12) = square root of (50)
Substract them to get minimum magnitude. (2i+3j) – (5i-2j) = – 3i+ 5j
Hence minimum magnitude = square root of [(-3)2 + 52) = square root of (34) | 259 | 732 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.53125 | 4 | CC-MAIN-2021-31 | latest | en | 0.651124 |
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Prev Next | 1,117 | 4,520 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.65625 | 3 | CC-MAIN-2018-22 | latest | en | 0.900142 |
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If f(x) = (1 + x)/(1 - x) Prov...
# If f(x) = (1 + x)/(1 - x) Prove that ((f(x) f(x^(2)))/(1 + [f(x)]^(2))) = (1)/(2)
Khareedo DN Pro and dekho sari videos bina kisi ad ki rukaavat ke!
Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.
Transcript
hello students today's question as if f of x is equal to 1 + X upon 1 minus x prove that f of X into f of x square whole divided by 1 + effects whole square is equal to 1 by 2 with the solution in the question we are given the value for f = 1 + X upon 1 minus x and y are also find this equal to this ok sunao was put the value in the above equation the equation is f of X into x square upon 1 + f of X whole square if x is equal to 1 + X upon 1 minus x to the value for f
of x square equal to 1 + x square upon 1 minus x square ok now we have to just put these values in the questions so we will get this will be equal to half of excess of this we will put here oneplus X upon 1 minus x Into X square + x square upon 1 minus x square and its wholly provided by this so 1 + F of whole square so it will be oneplus x divided by 1 - X whole square ok now this thing will be equal to numerator
female right as it is this a path for head will become 1 + X into 1 + x square as it is now its denominator we can make some changes here we have 1 - X and have 1 - x square with this thing we can open it with the help of Identity a minus A square minus b square which is a minus b and a + b into so listing will become 1 - x square 1 - X into 1 + x square minus x whole square into 1 + X this we have done now nominate apart this first numerator part we will get will take care LCM so it will become
1 - X whole square to open like 1 - 2x plus x square + 1 + distinct 2 X + x square this whole divided by 1 - X whole square song for the simplification here we will get oneplus X into 1 + x square into 1 minus x whole square divided by 1 minus x whole square into 1 + X into 2 into 1 + x square ok this thing when you will simplify the Dominator so here the single core upward and this
will come down and this - 2 X + 2 X will get cancelled to have you have 2 + 2 x square into we have taken common one whole square will get cancelled between -64 square and here also oneplus X ful get cancelled advantage X and 1 - X square + 1 + x square will get cancelled 1 + x square is always I cancel severe left with 1 by 2 and this thing is equal to what this thing is equal to of X into f of x square / one plus f of x square equal to 1 by 2 Hans fruit thank you | 719 | 2,636 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.15625 | 4 | CC-MAIN-2023-06 | latest | en | 0.92111 |
https://webwork.maa.org/wiki/PeriodicAnswers1 | 1,627,145,535,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046150307.84/warc/CC-MAIN-20210724160723-20210724190723-00577.warc.gz | 585,971,869 | 6,447 | Click to enlarge
This PG code shows how to check student answers that are periodic.
PG problem file Explanation
Problem tagging:
DOCUMENT();
"PGstandard.pl",
"MathObjects.pl",
);
TEXT(beginproblem());
Initialization:
Context("Numeric");
$answer = Real("pi/2")->with(period=>pi); Setup: This is self-explanatory. Context()->texStrings; BEGIN_TEXT Enter a solution to $$\cos(\theta) = 0$$.$BR
$BR $$\theta =$$ \{ ans_rule(10) \} \{ AnswerFormatHelp("angles") \} END_TEXT Context()->normalStrings; Main Text: $showPartialCorrectAnswers = 1;
the angle is an integer multiple of $$\pi$$. | 155 | 598 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2021-31 | latest | en | 0.583052 |
https://ch.mathworks.com/matlabcentral/cody/problems/497-make-an-awesome-ramp-for-a-tiny-motorcycle-stuntman/solutions/571248 | 1,603,870,894,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107897022.61/warc/CC-MAIN-20201028073614-20201028103614-00662.warc.gz | 247,505,939 | 17,096 | Cody
# Problem 497. Make an awesome ramp for a tiny motorcycle stuntman
Solution 571248
Submitted on 1 Feb 2015 by Debopam
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
%% v = [1 3 6 9 11]; y_correct = [1 3 6 9 11; 3 6 9 11 0; 6 9 11 0 0; 9 11 0 0 0; 11 0 0 0 0]; assert(isequal(vrooom(v),y_correct))
i = 2 ramp = 1 3 6 9 11 d = 0 w = 3 6 9 11 0 ramp = 1 3 6 9 11 3 6 9 11 0 i = 3 d = 0 0 0 0 w = 6 9 11 0 0 ramp = 1 3 6 9 11 3 6 9 11 0 6 9 11 0 0 i = 4 d = 0 0 0 0 0 0 0 0 0 w = 9 11 0 0 0 ramp = 1 3 6 9 11 3 6 9 11 0 6 9 11 0 0 9 11 0 0 0 i = 5 d = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 w = 11 0 0 0 0 ramp = 1 3 6 9 11 3 6 9 11 0 6 9 11 0 0 9 11 0 0 0 11 0 0 0 0 i = 6
2 Pass
%% v = [1 2 3]; y_correct = [1 2 3; 2 3 0; 3 0 0]; assert(isequal(vrooom(v),y_correct))
i = 2 ramp = 1 2 3 d = 0 w = 2 3 0 ramp = 1 2 3 2 3 0 i = 3 d = 0 0 0 0 w = 3 0 0 ramp = 1 2 3 2 3 0 3 0 0 i = 4
3 Pass
%% v = [-1 0 2 8]; y_correct = [-1 0 2 8; 0 2 8 0; 2 8 0 0; 8 0 0 0]; assert(isequal(vrooom(v),y_correct))
i = 2 ramp = -1 0 2 8 d = 0 w = 0 2 8 0 ramp = -1 0 2 8 0 2 8 0 i = 3 d = 0 0 0 0 w = 2 8 0 0 ramp = -1 0 2 8 0 2 8 0 2 8 0 0 i = 4 d = 0 0 0 0 0 0 0 0 0 w = 8 0 0 0 ramp = -1 0 2 8 0 2 8 0 2 8 0 0 8 0 0 0 i = 5
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Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A004280 2 together with the odd numbers (essentially the result of the first stage of the sieve of Eratosthenes). 21
1, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,2 COMMENTS Number of Fibonacci binary words of length n and having no subword 1011. A Fibonacci binary word is a binary word having no 00 subword. Example: a(5) = 9 because of the 13 Fibonacci binary words of length 5 the following do not qualify: 11011, 10110, 10111 and 01011. - Emeric Deutsch, May 13 2007 a(1) = 1; for n > 1, a(n) = least number > a(n-1) which is a unique sum of two earlier terms, not necessarily distinct. - Franklin T. Adams-Watters, Nov 01 2011 REFERENCES F. S. Roberts, Applied Combinatorics, Prentice-Hall, 1984, p. 256. LINKS Borys Kuca, Structures in Additive Sequences, arXiv:1804.09594 [math.NT], 2018. See V(1,2). H. B. Meyer, Eratosthenes' sieve Index entries for linear recurrences with constant coefficients, signature (2,-1). FORMULA G.f.: x(1+x^3)/(1-x)^2; a(n) = 2n - 3 + C(1, n-1) + C(0, n-1). - Paul Barry, Mar 05 2007 a(n) = 2*n - 3 + floor(2/n). - Wesley Ivan Hurt, May 23 2013 MAPLE 1, 2, seq(2*n-1, n=2..66); # Emeric Deutsch, May 13 2007 MATHEMATICA Union[ Join[ 2Range[65] - 1, {2}]] (* Robert G. Wilson v *) PROG (PARI) a(n)=2*n + 2\n - 3 \\ Charles R Greathouse IV, Nov 01 2011 CROSSREFS Cf. A002858. Sequence in context: A186330 A153809 A004274 * A053224 A277334 A091377 Adjacent sequences: A004277 A004278 A004279 * A004281 A004282 A004283 KEYWORD easy,nonn AUTHOR EXTENSIONS Offset changed to 1 and formulas updated accordingly (at the suggestion of Michel Marcus) by Charles R Greathouse IV, Sep 03 2013 STATUS approved
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Last modified October 17 00:03 EDT 2019. Contains 328103 sequences. (Running on oeis4.) | 881 | 2,403 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.625 | 4 | CC-MAIN-2019-43 | latest | en | 0.655673 |
https://blog.mie-solutions.com/shop-rates/how-to-manufacturing-hourly-rate-calculation | 1,558,836,617,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232258620.81/warc/CC-MAIN-20190526004917-20190526030917-00453.warc.gz | 406,747,540 | 14,294 | • # MIE Solutions Blog
Sheet metal, CNC shops, machine shops and many other job shops provide a valuable service to their customers. For a job shop to be a profitable business, the service rate should cover the cost of doing business plus have a certain amount of margin or profit built into the price customers pay. If this is too low, you will be gaining new work but this will only last as long as you have money in the bank. You business will fail because the owner needs to earn an income. If the price is too high, customers will choose a competitor. Some high level ways to calculate your hourly shop rate is shown below. Hourly rate calculations are not that complicated but should be looked at carefully in order to be a profitable company.
## Equipment
1. Calculate the cost per hour of operation and include a markup for maintenance hours in your calculation to determine a fully burdened cost per machine hour. The formula is: (machine purchase cost + expected lifetime maintenance cost) / expected hours of operating life. You can choose to do this per machine or an average of all machines.
2. ## Labor
3. Develop an hourly shop rate: (total annual labor costs + taxes + benefits + paid time off) / (total annual hours worked - breaks and training time). This is your direct labor cost per hour.
5. Any costs not directly involved in machining a part is overhead. These include costs for administrative staff salary, equipment, furniture, building lease, maintenance and office supplies. Calculate the annual costs of these, then divide by total labor or machine hours for the year. This will be your overhead cost per hour.
6. ## Markup
7. Here's where the shop earns its keep. The owner's income and future growth for the shop depends on this calculation working well. Simple calculation is markup = 1 + (owner's salary + benefits + annual earnings goal) / annual service hours) / (machine + labor + overhead cost per hour). Converted to a percentage, for example, this will come to something like 120 percent, basically adding 20 percent profit to the cost of doing business.
8. ## Service Rate Calculation - Average Rate
9. Use this formula when your machine costs are fairly similar from one piece of equipment to another: Average overall shop rate = (average machine cost per hour + labor and overhead cost per hour) x markup x total hours for the job.
10. ## Service Rate Calculation - Machine-Specific Rate
11. Use this formula when cost of equipment varies greatly from piece to piece and not all machines are used in each service. Rate = (specific machine(s) cost per hour + labor & overhead cost per hour) x markup x total hours for the job.
MIE Solutions offers a made to order job shop ERP system designed for the manufacturer of goods and products. Most accounting systems are designed for the basic AR, AP and GL side of financials where a manufacturing software product deals with the actual production of the goods and services. MIE Trak is a full featured ERP system for the made to order and engineer to order manufacturer.
http://www.mie-solutions.com | 649 | 3,103 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.140625 | 3 | CC-MAIN-2019-22 | longest | en | 0.936442 |
https://bayareamath.wordpress.com/2016/02/ | 1,498,695,442,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128323808.56/warc/CC-MAIN-20170629000723-20170629020723-00419.warc.gz | 732,595,263 | 33,120 | # Worksheets
This week in my precalculus class I used two worksheets that seemed to engage my students more than other worksheets have in the past. The topic was piecewise functions, functions formed by partitioning a domain into subdomains, or pieces, each of which piece is then associated with a dedicated function. For example, for a hypothetical parking lot, charges for the first hour could be \$10 dollars, the second hour \$8, and every hour after that \$5, up to 24 hours (with partial hours rounded to the next hour). The function to calculate total charge for parking could be represented as follows,
P(h)={
10 if 0<h≤1
10+8 if 1<h≤2
10+8+5(ceiling(h)-2) if 2<h≤24
}
To find the charge for 4.5 hours the function would be evaluated as follows,
0<4.5≤1 is false
1<4.5≤2 is false
2<4.5≤24 is true
therefore,
f(4.5) = 10+8+5(5-2) = \$33
The piecewise function has two parts, the right-most part that specifies qualifying conditions and the left-most part that specifies a dedicated function to evaluate, if its associated condition is met. That is, the unique condition in the right-hand part, that evaluates to true for the input to the function, identifies its corresponding dedicated function in the left-hand part as the appropriate function to evaluate the input. In this case, as shown above, the condition that is true given 4.5 as an input is the condition in the last line of the function specification. Therefore, the function is evaluated with input 4.5 using (10+8+5(ceiling(h)-2)) as the relevant dedicated function, returning an answer of \$33.
The details really are not important, except as a setting for my reflection.
The first worksheet presented several definitions of piecewise functions, similar to what was just shown. For each of the functions the students needed to graph the piecewise function and then evaluate the function for several input values, both algebraically and graphically. We spent approximately 15 minutes before the exercise going over how to graph piecewise functions on a TI-84 calculator so the students were testing that new knowledge at the same time as they were testing their understanding of the evaluation of piecewise functions. All of the students participated, some in small groups, some alone. I wandered the classroom looking over their shoulders and answering questions. They appeared to all be in search of answers to the worksheet problems. From the questions I received from some of the students, it was clear that not all of the students had really understood my explanations of piecewise functions, even with examples still on the board. This has become a common enough result that I am convinced that in my classroom of 40 students, from so many different backgrounds, there will always be some students that will not understand my lecture in the way that I think they should. More individual attention will apparently always be needed for some students. The in-class worksheet approach seems to provide a good way to identify at least some of the students in need.
The second worksheet presented two application problems, one about age-based pricing at a buffet restaurant and the other about the time (in minutes) that a person may safely scuba dive at a certain depth without having to decompress while surfacing—depth in feet. The second worksheet was an in-class project on the day after the first worksheet project. I lectured on some examples of application problems before distributing the second worksheet. The students worked with interest but again I received questions that showed a lack of understanding of what I had explained in the lecture. To be sure, most students had no problem establishing the correct form of the piecewise functions for both problems, but almost all of them had some trouble in accurately completing each form so that each result was a piecewise function and not just a piecewise relation. What that exactly means is not important here.
In summary, I think that each worksheet was a good, active learning experience for both the students and for me. And again, the in-class worksheets made me confront the reality that no matter what information I think I am transmitting in my lectures, not all students are receiving the intended message.
# Bits and Pieces
This week, rather than reflect on a topic in teaching, I’m just going to list bits and pieces of my teaching environment that I someday need to think about, do about, or forget about.
1. I am teaching introductory calculus this quarter, the first section of four, and the focus is on differentiation. While wandering the internet I came across an online differentiation calculator that can easily differentiate all of the standard equations that I generally assign for homework practice. It will even show the steps that were followed. So it begs the question, why assign equations for students to differentiate for homework? And why ask them to show their work?
2. I generally write my lesson plans, quizzes, tests, worksheets, etc., in MSWord using its mathematical editing application. It has worked very well for me in the past; I’ve been using it for years. Last week, however, MSWord began to inexplicably slow down after I was editing one of my files with a lot of tables with embedded graphs, text, and mathematical equations. I would type and nothing would happen on the screen. Some 10s of seconds later, my typing would begin to display. Needless to say this is not an acceptable way to work. I ran some searches to see if anyone else had the problem and might suggest a solution. I found some references to Windows 7 and Office 2013 showing this problem, but the references were several years old. I read through some of the suggestions, and tried a few that did not require editing the registry, but no luck. Editing still seems to slow down at unpredictable times on larger files with lots of tables. I then had the school’s help desk look at the problem, but the best they could suggest was that I clean up my trash bin and temporary files and defragment the disk. None of that did anything to fix the problem. So I’ll have to think more about this next week. Oddly enough, I have Windows 7 and MSWord on my home computer, but the same files do not create the same problem.
3. I’ve been struggling with testing and grading this quarter. It just seems to take too much time to prepare weekly quizzes or tests, including answer sheets, and then grade the weekly quizzes or tests for 100 students. I want to offer weekly assessments to keep the students engaged, but it’s really becoming too much work for me. I have been avoiding multiple choice questions, but I may be forced to try them. However, it is always more work to change methods in mid-stream so I’ll wait until next quarter to begin the change. Of course I’ve been warned that the preparation of good multi-choice tests can be as time consuming as the preparation of any other type of assessment.
4. This week I had trouble following the work of a student on a quiz. The flow of mathematical argument seemed to make sense, and then, suddenly, it didn’t. It takes concentration and time to try to guess why a student suddenly drops exponents in a differentiation when there is no logical reason for dropping them. Some rules of differentiation can have that effect, but the context didn’t call for the rules. I stopped and wrote a note to the student to go through my online solution to the quiz and then get back to me with questions. Maybe he can figure out what he’s doing, or not doing.
5. No matter how much I discourage the question, students just can’t seem to resist: “Is this going to be on the quiz?” Maybe I should take those questions as a message to me about my teaching, my lesson structure, my rules of engagement. Or maybe I should always just answer “yes.”
# A Question about a Question
In a recent email a colleague wrote the sentence, “The ability to read simple directions seems to be a dying art among students.” The context made it clear that he was jesting, but I was struck by the sentence because I had just finished grading a quiz in which a majority of my students had misread what I considered a simple direction. The question that was misread was the following:
1. (6 points) If you invested \$5,500 in a banking account, what is the final balance in the account and the amount of interest paid after 4 years if you earn:
1a. 1.7% interest compounded annually?
1b. 0.7% interest compounded continuously?
For this question, I expected the students to calculate two dollar amounts for each of parts 1a and 1b. One dollar amount giving the balance in the account after 4 years and one dollar amount giving the interest earned in the account after 4 years. Of the 32 students who took the quiz, only eight answered with both the balance and the interest earned while 24 students answered with only the balance.
Although it is tempting for me to dismiss the result as students moving too quickly through the quiz, I am afraid that there must be more to this than just the students’ direction-reading abilities. After all, more than 70% of the students missed the cue. There must be something about the question that is broken. My current thought is that students forgot about the interest part of the question because what they were accustomed to calculating in class was the final balance. We may have looked at interest apart from balance a few times, but the majority of practice was in calculating final balance. I presume they mentally closed the question once they found the balance, and moved on.
If that, possibly, is what happened, how should I rephrase the question to make both parts of the question more memorable after the balance calculation? Should I provide fill-in prompts for each of parts 1a and 1b, one prompt for final balance and another for interest earned? Should I explicitly rewrite the question to emphasize its two parts? For example,
1. (6 points) If you invested \$5,500 in a banking account, what is the final balance of the account and what is the final amount of interest paid into the account after 4 years, if you earn:
1a. 1.7% interest compounded annually?
1b. 0.7% interest compounded continuously?
Or should I rewrite the one multi-layered question as multiple different questions? Or should I provide a fill-in-the-blanks answer table. Or is there something else I should do? More work for me, but the question about the question needs to be answered.
And one more thought. It was not a good idea to use 1.7% in part 1a and 0.7% in part 1b. A few students answered both questions using 1.7%. I’m sure it’s one of those tricks the brain plays when in fills in what it expects to see, rather than what is written.
Until next week.
# Lessons on Lesson Planning
Today I’d like to reflect on lesson structure and lesson preparation. In the past I’ve prepared for a lecture by writing lecture notes on 8 ½ x 11 notepaper. The notes would be structured to include, in order, all the topics I wanted to cover that lecture period. The notes would also include examples for me to develop at the board and a short exercise for students to work on after I completed my examples. When students finished the exercise I would poll them for answers—usually there were 2-3 different answers called out. Once all the answers were taken I would walk (figuratively) through the exercises with the students, as a class, noting the places where wrong answers were creeping in. Then, if there were no questions, on to the next topic.
As I’ve written in an earlier blog, I’ve being trying to change my lesson structure to make my lessons more active. I have been including worksheets in my lesson structure, with more complicated questions on the worksheets, in place of the simple in-class exercises I was previously using. The worksheets have about 15-20 minutes of material in them and they normally require a student to interpret English-language descriptions of problems, rather than just mathematical formulas. As the students work on the material, alone or in groups, their choice, I circulate and answer questions. So far, the change is helping me to work more directly with students who are having trouble with the questions—either the math or the interpretation of the English description. These students did not self-identify as having problems when I was using the older structure of embedded, single-exercise check-ups on understanding. I’m positive on the changes so far. Unfortunately, I haven’t been doing this long enough to say much more about it right now.
Another change I’ve started is to enter my notes in outline form in computer files. The advantage is that I can hope to create an improving body of lesson plans as I teach and reteach the same courses. The disadvantage is the time it takes to format the lesson plans online—I’m accustomed to thinking with paper and pen. It’s also time consuming to generate graphs and tables that are simple to do by hand, but not always so simple in a word processor. Some instructors scan in hand-draw diagrams to get the best of both worlds, but I haven’t tried to do that yet.
I have, from the beginning, created my worksheets online. It’s also a time consuming process, especially since I create an answer sheet to share with the students. (Unless I just run out of time. Then the students have to be satisfied with in-class answers.) I do like having the growing body of worksheets, but I now need to give more thought to how I name the files, since I’ve already experienced retrieval problems and I’ve only just started with this method.
For now, I have to return to lesson planning. More next week. | 2,897 | 13,709 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4 | 4 | CC-MAIN-2017-26 | longest | en | 0.917287 |
http://mathhelpforum.com/pre-calculus/157333-expression-representing-following-function-print.html | 1,524,252,906,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125944677.39/warc/CC-MAIN-20180420174802-20180420194802-00352.warc.gz | 208,320,604 | 3,237 | # An expression representing the following function...
• Sep 24th 2010, 06:51 PM
VectorRun
An expression representing the following function...
So I'm stuck on this question: find an expression for the function whose graph is the bottom half of the parabola, $\displaystyle x+(y-3)^2=0$. It should be expressed in terms of x according to the text that I'm working from.
The problem I'm having is actually isolating y without encountering a negative square root...Now, I haven't learned how to deal with complex numbers much so I'm not sure if that's the only way to do this. If it's possible to do this normally, could I have some hints?
• Sep 24th 2010, 06:53 PM
Prove It
If you're expressing it in terms of $\displaystyle x$ then
$\displaystyle x = -(y - 3)^2$.
• Sep 24th 2010, 06:56 PM
VectorRun
Oops, I meant expressing it as y in terms of x so that's it's $\displaystyle y=$
• Sep 24th 2010, 07:23 PM
Prove It
$\displaystyle (y - 3)^2 = -x$
$\displaystyle y - 3 = \pm \sqrt{-x}$
$\displaystyle y = 3 \pm \sqrt{-x}$.
If you want the lower half then only accept
$\displaystyle y = 3 - \sqrt{-x}$.
• Sep 24th 2010, 07:28 PM
VectorRun
Oh, is that really an acceptable answer? I got that but I wasn't sure if it was right due to the negative radicand...I guess I got thrown off by all the teachers always saying it's a big no-no. Thanks a lot.
• Sep 24th 2010, 07:29 PM
Prove It
Is $\displaystyle -x$ always a negative number?
• Sep 24th 2010, 07:47 PM
VectorRun
I know it isn't when it's either 0 or a negative number but I was only thinking about the notation so I didn't really concern myself with anything else...Plus, the question didn't really allow us to write a domain.
• Sep 24th 2010, 07:50 PM
Prove It
Quote:
Originally Posted by VectorRun
I know it isn't when it's either 0 or a negative number but I was only thinking about the notation so I didn't really concern myself with anything else...Plus, the question didn't really allow us to write a domain.
Doesn't matter, there's such a thing as an implied domain. There's nothing wrong with the notation as long as it's possible for any value of $\displaystyle x$. | 607 | 2,135 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.84375 | 4 | CC-MAIN-2018-17 | latest | en | 0.946334 |
https://savvycalculator.com/shipping-cost-per-pound-calculator/ | 1,713,666,282,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817699.6/warc/CC-MAIN-20240421005612-20240421035612-00816.warc.gz | 458,041,909 | 46,491 | # Shipping Cost Per Pound Calculator
## Introduction
Shipping goods efficiently and cost-effectively is a priority for businesses engaged in e-commerce, retail, manufacturing, and various other industries. Understanding the cost of shipping per pound of goods is crucial for pricing strategies, budgeting, and optimizing shipping processes. The Shipping Cost Per Pound Calculator simplifies this complex task, allowing businesses and individuals to make informed decisions regarding shipping expenses.
## Formula:
The formula for calculating the Shipping Cost Per Pound is relatively straightforward:
Shipping Cost Per Pound = Total Shipping Cost / Total Weight (in pounds)
Where:
• Shipping Cost Per Pound represents the cost of shipping per pound of goods.
• Total Shipping Cost is the overall cost incurred for shipping the goods.
• Total Weight (in pounds) is the combined weight of all the goods being shipped, measured in pounds.
This formula provides a clear and concise way to determine how much it costs to ship one pound of goods.
## How to Use?
Using the Shipping Cost Per Pound Calculator involves the following steps:
1. Gather Shipping Data: Collect all relevant shipping data, including the total cost of shipping and the total weight of the goods being shipped. Ensure that you measure weight in pounds.
2. Access the Calculator: Open the Shipping Cost Per Pound Calculator on your preferred device, whether it’s a computer, smartphone, or an online tool.
3. Input Shipping Data: Enter the total shipping cost and the total weight of the goods in pounds into the calculator.
4. Calculate Shipping Cost Per Pound: Click the calculate button or perform the calculation manually using the formula:
Shipping Cost Per Pound = Total Shipping Cost / Total Weight (in pounds)
5. Interpret the Result: The calculated Shipping Cost Per Pound is the cost associated with shipping one pound of goods. This information is valuable for pricing decisions, budgeting, and evaluating shipping efficiency.
6. Optimize Shipping Strategies: Use the calculated cost per pound to assess the efficiency of your current shipping methods. Explore opportunities to reduce shipping costs, negotiate better rates with carriers, or adjust pricing strategies as needed.
## Example:
Let’s illustrate the Shipping Cost Per Pound Calculator with a practical example:
Suppose a small e-commerce business shipped a package weighing 25 pounds, and the total shipping cost for that package was \$50. To calculate the Shipping Cost Per Pound, you would use the formula:
Shipping Cost Per Pound = Total Shipping Cost / Total Weight (in pounds)
Shipping Cost Per Pound = \$50 / 25 pounds
Shipping Cost Per Pound = \$2 per pound
In this example, the calculated Shipping Cost Per Pound is \$2. This means that it costs \$2 to ship one pound of goods. Businesses can use this information to make informed decisions about shipping expenses, pricing, and cost management.
## FAQs?
1. Why is calculating the Shipping Cost Per Pound important for businesses? Calculating the Shipping Cost Per Pound is essential for businesses to understand their shipping expenses accurately. It aids in pricing strategies, budgeting, and optimizing shipping processes.
2. How can businesses reduce their Shipping Cost Per Pound? Businesses can reduce their Shipping Cost Per Pound by negotiating better shipping rates with carriers, optimizing packaging to reduce weight, using efficient shipping methods, and implementing cost-effective shipping strategies.
3. Does the Shipping Cost Per Pound vary for different shipping methods? Yes, the Shipping Cost Per Pound can vary depending on the chosen shipping method, carrier, package dimensions, and destination. It’s important to analyze different shipping options to find the most cost-effective solution.
## Conclusion:
The Shipping Cost Per Pound Calculator is a valuable tool for individuals and businesses involved in shipping goods. Accurate knowledge of the cost of shipping per pound enables efficient pricing strategies, budgeting, and cost management. In an increasingly competitive marketplace, optimizing shipping expenses is essential for maintaining profitability and providing customers with cost-effective shipping options. By using the Shipping Cost Per Pound Calculator, businesses can make data-driven decisions, reduce shipping costs, and enhance their competitiveness in the world of commerce. | 803 | 4,443 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.015625 | 3 | CC-MAIN-2024-18 | longest | en | 0.903156 |
https://www.freshers.in/learn/c_programming/arithmetic-operators-in-c/ | 1,718,968,037,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862070.5/warc/CC-MAIN-20240621093735-20240621123735-00655.warc.gz | 681,821,883 | 18,717 | # Arithmetic Operators in C
Programming in the C language often begins with mastering its fundamental building blocks, and arithmetic operators are among the most crucial. In this article, we’ll delve into the basics of C programming by exploring the commonly used arithmetic operators: addition (+), subtraction (-), multiplication (*), division (/), and modulus (%). Through real-world examples and detailed explanations, you’ll gain a solid understanding of how to use these operators effectively. Understanding the basics of C programming, such as arithmetic operators, is essential for any aspiring programmer. In this article, we’ve explored the fundamental arithmetic operators in C (+, -, *, /, and %) with real-world examples and their respective outputs. Armed with this knowledge, you’re ready to tackle more complex programming tasks and build powerful C applications. Practice and experimentation are the keys to becoming proficient in C programming, so don’t hesitate to explore further and refine your skills.
The addition operator (+) is used to add two or more values together. Let’s look at a simple example:
#include <stdio.h>
int main() {
int num1 = 10;
int num2 = 5;
int result = num1 + num2;
printf("The sum of %d and %d is %d\n", num1, num2, result);
return 0;
}
Output:
The sum of 10 and 5 is 15
## Subtraction (-)
The subtraction operator (-) is used to subtract one value from another. Here’s an example:
#include <stdio.h>
int main() {
int num1 = 15;
int num2 = 7;
int result = num1 - num2;
printf("The difference between %d and %d is %d\n", num1, num2, result);
return 0;
}
Output:
The difference between 15 and 7 is 8
## Multiplication (*)
The multiplication operator (*) is used to multiply two or more values. Take a look at this example:
#include <stdio.h>
int main() {
int num1 = 8;
int num2 = 4;
int result = num1 * num2;
printf("The product of %d and %d is %d\n", num1, num2, result);
return 0;
}
Output:
The product of 8 and 4 is 32
## Division (/)
The division operator (/) is used to divide one value by another. Here’s an example:
#include <stdio.h>
int main() {
int num1 = 20;
int num2 = 5;
float result = (float)num1 / num2;
printf("The result of %d divided by %d is %.2f\n", num1, num2, result);
return 0;
}
Output:
The result of 20 divided by 5 is 4.00
## Modulus (%)
The modulus operator (%) is used to find the remainder when one value is divided by another. Let’s see it in action:
#include <stdio.h>
int main() {
int num1 = 17;
int num2 = 5;
int result = num1 % num2;
printf("The remainder of %d divided by %d is %d\n", num1, num2, result);
return 0;
}
Output:
The remainder of 17 divided by 5 is 2
Author: user | 692 | 2,695 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.359375 | 3 | CC-MAIN-2024-26 | latest | en | 0.840488 |
https://tex.stackexchange.com/questions/157063/can-you-fix-this | 1,723,736,074,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641299002.97/warc/CC-MAIN-20240815141847-20240815171847-00784.warc.gz | 432,695,170 | 37,820 | # can you fix this?
Can you fix this? There are several horrors!
\begin{tabular}{ | c | c | c | c | }
\hline
Modelo & Gl & SC & F \\
\hline
\beta'=(\beta_0,\beta_1) & 2 & \beta'X'Y & $\frac{(SSE_r-SSEc)/(k-g)}{SSE_c/(n-[k+1])}$\\
Residual & n-2 & Y'Y-\beta'X'Y & \\
\hline
Total & n & \textbf{Y'Y} & asd\\
\hline
\end{tabular}
• Please have a look on our starter guide to familiarize yourself further with our format- at the moment it doesn't quite fit :) Commented Feb 1, 2014 at 21:29
\beta can be used only in mathmode. Here is a way of coding – but I'm unsure of what is supposed to be maths formulae, what is supposed to be text. I use the cellspace package to have a minimal distance between the top of the contents of a cell and the line above, and similarly between the bottom of the contents and the line below:
\documentclass[11pt, a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{mathtools, array, bm}
\DeclareMathOperator{\SSE}{SSE}
\usepackage[math]{cellspace}
\cellspacetoplimit=4pt
\cellspacebottomlimit=4pt
\usepackage{lmodern}
\begin{document}
$\renewcommand{\arraystretch}{1.5} \begin{array}{ | *{4}{Sc|}} \hline \text{Modelo} & Gl & SC & F \\ \hline \beta'=(\beta_0,\beta_1) & 2 & \beta'X'Y & \dfrac{(\SSE_r-\SSE_c)/(k-g)}{\SSE_c/(n-[k+1])}\\ \text{Residual} & n-2 & Y'Y-\beta'X'Y & \\ \hline \text{Total} & n & \bm{Y'Y} & \text{asd}\\ \hline \end{array}$
\end{document}
Result:
• Envoke \DeclareMathOperator*{\SSE}{SSe} and then use \SSE. Also, \text{Residual } should be \text{Residual}. Commented Feb 9, 2014 at 9:45
• Btw. I guess that Gl and SC are also operators. Commented Feb 9, 2014 at 10:22
• @Svend Tveskæg: Thanks. Fixed it, and corrected \SSE c to \SSE_c (seems to be a typo). Commented Feb 9, 2014 at 10:23
• @Svend Tveskæg: Do you think so? That doesn't seem very consistent with the labelling of the row. Commented Feb 9, 2014 at 10:29
• Hmmm. That's a good point. :) Commented Feb 9, 2014 at 10:30 | 731 | 2,018 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2024-33 | latest | en | 0.735209 |
http://slidegur.com/doc/22863/simple-machines | 1,477,267,622,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988719453.9/warc/CC-MAIN-20161020183839-00502-ip-10-171-6-4.ec2.internal.warc.gz | 234,137,622 | 8,545 | ### Simple Machines
```ACADs (08-006) Covered
1.1.2.4.2
1.1.2.6.2
Keywords
Levers, gears, cams, pulleys, physics terms, units, mechanical principles, efficiency, machine
Description
This PowerPoint presentation can be used to train people about the basics of simple
machines. The information on the slides is the minimum information that should be
explained. The trainer notes for each slide provide more detailed information, but it is up to
the trainer to decide how much of this information is presented in class. The notes are
Supporting Material
Augusta Technical College
2011
Objectives
Explain and use physics terms, units, mechanical principles,
mechanical definitions and basic concepts
Learning Outcomes:
1. Explain the mechanical principles:
Including the functions of simple machine individual
components
Such as: Levers, Gears, Cams & Pulleys
Energy efficiency opportunities
Augusta Technical College
2011
Simple Machines
What are “simple machines”?
•
A device for increasing or decreasing the amount of applied
force in opposition to a resisting force
•
The “applied force” is called effort or effort force, labeled:
Fe
•
The “resistive force” is called resistance , labeled:
Fr
Augusta Technical College
2011
Force NOT Energy
Important to note the definition uses:
•
FORCE not ENERGY
•
The energy, or work, out can not exceed the energy input
•
Something must be sacrificed for the simple machine to change
the amount of effort required
Augusta Technical College
2011
Inclined Plane
Exchanges more distance or speed for less effort
Augusta Technical College
2011
Wedge
{ Dual Inclined Plane }
Exchanges more distance for less effort
Augusta Technical College
2011
Zipper-The Plane at Work
Wedges for opening and closing
Augusta Technical College
2011
Wedges Applied—Cam and Follower
Augusta Technical College
2011
The Wrench –Wheel and Axle
Augusta Technical College
2011
The Wrench –Wheel and Axle
Augusta Technical College
2011
The Wrench –Wheel and Axle
Wheel --shorter but more powerful movement at the axle
Augusta Technical College
2011
Gears
Convert rotational motion by
• changing direction
Gears can be meshed together to
•Multiply force or speed and distance
Speed is gained at the expense of effort
Augusta Technical College
2011
Levers
Augusta Technical College
2011
Pulleys
Augusta Technical College
2011
Pulley – Block and Tackle
MA = 2
MA = 3
Augusta Technical College
MA = 3
2011
MA = 4
Simple Machines of Everyday
Where are the “simple machines” in your life?
• Scissors
• Wrenches
• Can openers
• Car jacks
• Wheelbarrows
• Car starter motors
Augusta Technical College
2011
Complex Machines of Everyday
Where are the “simple machines” in your life?
Activity - simple-machines
Power tools and other complex machinery
- made up of combinations of “simple machines”
Augusta Technical College
2011
Mechanical Efficiency
• Very few machines ever work in an ideal fashion
• Actual resistance by the actual effort applied, you find the
• Part of your effort goes into overcoming the internal friction
of the machine
Augusta Technical College
2011
Mechanical Efficiency
• By reducing friction you can improve the mechanical
efficiency of any machine
• You will never be able to eliminate friction entirely
• Although simple machines are all less than perfect in this
respect, using them properly will make your work much easier
Augusta Technical College
2011
What Did We Learn?
Augusta Technical College
2011
Simple Machines
Q&A
Augusta Technical College
2011
``` | 854 | 3,493 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.84375 | 3 | CC-MAIN-2016-44 | latest | en | 0.816423 |
http://unizor.blogspot.com/2011/10/ | 1,531,971,830,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676590493.28/warc/CC-MAIN-20180719031742-20180719051742-00327.warc.gz | 373,807,522 | 11,689 | ## Monday, October 10, 2011
### Construction Problems in Geometry
Construction problems in geometry are extremely important. They help to develop student's creativity, logical thinking and ability to combine analysis of a problem at hand with synthesis of existing methods into concrete solution. Solving problems is the most important purpose of UNIZOR.COM. Please examine these problems and try to solve them. The accompanying lecture contains all the solutions, but watch it only after you spent sufficient amount of time trying to solve these problems yourself.
1. Construct a sum of two angles.
In details, this construction problem has the following meaning, applicable to other problems as well (so, we will not repeat it).
Given two angles and a ray somewhere on a plane.
Using a given ray as one leg, construct another ray from the same starting point such that these two rays (one given and one constructed) form an angle, which has a measure equal to a sum of measures of two given angles.
2. Construct a difference between a bigger and a smaller angle.
3. Given a sum and a difference between two angles, construct these angles.
4. Divide an angle into 4, 8 and 16 congruent parts.
5. Construct a triangle by its two sides and an angle opposite to a bigger side.
Is it always a unique triangle? Analyse the number of solutions of this problem.
6. Construct a triangle by its two sides and an angle opposite to a smaller side.
Is it always a unique triangle? Analyse the number of solutions of this problem.
7. Construct an isosceles triangle by a base (a side, generally speaking, non-congruent to two others) and one of two other sides.
8. Construct an isosceles triangle by a base (a side, generally speaking, non-congruent to two others) and one of two congruent angles (usually called angles at the base or base angles).
9. Construct an isosceles triangle by one of two congruent sides and an angle between congruent sides (usually called an angle at the vertex).
10. Construct an isosceles triangle by one of two congruent sides and a base angle it forms with a base (a side, generally speaking, non-congruent to two others).
11. Construct a right triangle by its two legs (i.e. sides, perpendicular to each other, sometimes called also catheti).
12. Construct a right triangle by one of its legs (also known as cathetus) and a hypotenuse.
13. Construct a right triangle by a cathetus and an acute angle it forms with a hypotenuse.
14. Construct an isosceles triangle by an altitude to a base and one of two congruent sides.
15. Construct an isosceles triangle by an altitude to a base and an angle opposite to a base (i.e. vertex angle).
16. Construct an isosceles triangle by a base and an altitude towards one of two congruent sides.
17. Construct a right triangle by a hypotenuse and an acute angle it forms with one of catheti.
18. Given an angle and a point inside it. Construct a straight line crossing this point and cutting congruent segments from sides of a given angle.
19. Construct two segments by their given sum and difference.
20. Divide a given segment into 4, 8 and 16 congruent parts.
21. Given a straight line and two points anywhere on a plane. Construct a point on a given line equidistant to two given points.
22. Construct a point equidistant to three vertices of a given triangle.
23. Given an angle and a straight line that crosses both its sides. Construct a point on this line equidistant to two sides of a given angle.
24. Construct a point equidistant to three sides of a given triangle.
25. Given a straight line PQ and two points M and N outside it, but on the same side from it. Construct a point X on the line PQ such that angles ∠PXM and ∠QXN are congruent.
26. Construct a right triangle by one of its catheti and a sum of hypotenuse and the other cathetus.
27. Construct a triangle by a side, an angle it makes with another side and a sum of two other sides.
28. Given an angle and two points, one on each side of an angle. Construct a point equidistant from both sides of an angle and, at the same time, equidistant from two given points on angle's sides.
Notice, that distances to angle's sides should be equal to each other, but not necessarily equal to distances to given points.
### Geometrical Problems
Finally, I've reached a point when I can start introducing problems in Geometry. Problems below are, mostly, from more than 100 years old textbook on geometry by a famous Russian math teacher Kiselev.
Solving problems is the most important purpose of our site UNIZOR.COM. Please examine these problems and try to solve them. The accompanying lecture contains all the solutions, but watch it only after you spent sufficient amount of time trying to solve these problems yourself.
1. Prove that in an isosceles triangle two medians to congruent sides are congruent.
2. Prove that in an isosceles triangle two angle bisectors to congruent sides are congruent.
3. Prove that in an isosceles triangle two altitudes to congruent sides are congruent.
4. Prove that segments of two perpendicular bisectors to two congruent sides of an isosceles triangle between midpoint of one side and crossing of its bisector with another side are congruent.
More precisely, consider an isosceles triangle ΔABC with congruent sides AB and BC. Draw perpendicular bisectors of its congruent sides through midpoint M of side AB and midpoint N of side BC. Point P is a crossing point of the perpendicular bisector of side AB with side BC. Point Q is a crossing point of the perpendicular bisector of side BC with side AB. Prove that segments MP and NQ are congruent.
5. Prove that a line, perpendicular to an angle bisector, cuts from two rays forming this angle congruent segments, assuming that an angle is less that 180 degrees.
In details, let AB and AC be two rays forming angle ∠BAC, let AM be a bisector of this angle and P - any point on this bisector. Draw a perpendicular to AM that croses it at point P. This same perpendicular crosses rays AB at point X and AC at point Y. Prove that segments AX and AY are congruent.
6. Prove that median AM of a triangle ΔABC from vertex A to an opposite side BC is equidistant from vertices B and C.
Notice, that distance from a point to a line is measured as a length of a perpendicular dropped from this point to a line.
7. Prove that the length of median AM of a triangle ΔABC from vertex A to an opposite side BC is less than half sum of lengths of sides AB and AC in lies in between.
Hint: extend the median beyond side BC by doubling its length to point D and consider triangle ΔABD.
8. Prove that sum of lengths of all three medians of a triangle is less than its perimeter, but greater than its halp-perimeter.
Hint: use the triangle inequality and the previous problem.
9. Prove that sum of lengths of two diagonals of a quadrangle is less than its perimeter, but greater than its half-perimeter.
10. Given an angle ∠PMQ and two points on each side: A and B on side MP and A' and B' on side MQ such that corresponding pairs of segments are congruent:
MA is congruent to MA' and MB is congruent to MB'.
Prove that crossing segments AB' and A'B cross on a bisector of angle ∠PMQ.
Notice, that this theorem implies an easy way to construct an angle bisector.
11. Given a sraight line PQ and two pairs of points symmetrical relative to this line: points A and A' are symmetrical relative to PQ, points B and B' are symmetrics too relative to the same line PQ.
Prove that there exists a point M on line PQ equidistant from all four points A, A', B and B'.
12. Given a straight line PQ and two points A and B on the same side from it. Find a point M on line PQ such that the sum of lengths of segments AM and MB is minimal.
13. Given an accute angle ∠PMQ and point A inside it. Find point X on side MP of this angle and point Y on its other side MQ such that a perimeter of triangle ΔAXY is minimal. | 1,825 | 7,932 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.375 | 4 | CC-MAIN-2018-30 | longest | en | 0.936573 |
http://www.jiskha.com/display.cgi?id=1339645089 | 1,495,854,013,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463608765.79/warc/CC-MAIN-20170527021224-20170527041224-00218.warc.gz | 705,514,987 | 3,806 | # physics
posted by on .
Two boys on skates push off from each other. The 40 kg boy moves to the left at 10 m/s. If the other boy moves to the right at 8 m/s, what is his mass?
• physics - ,
Momentum of the 'two boys' system shall be conserved (because there is no external force in the horizontal direction)
So, m1v1 = m2v2
m1 = 40*10/8 = 50 Kg
• physics - ,
Thank you | 114 | 376 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.421875 | 3 | CC-MAIN-2017-22 | latest | en | 0.898543 |
https://idoabramsohn.com/calculator-934 | 1,675,511,872,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764500126.0/warc/CC-MAIN-20230204110651-20230204140651-00640.warc.gz | 320,189,355 | 6,675 | # Help on math
Here, we will be discussing about Help on math. Let's try the best math solver.
## The Best Help on math
Help on math is a mathematical instrument that assists to solve math equations. A parabola solver is a mathematical tool used to find the roots of a quadratic equation. A quadratic equation is any equation that can be written in the form ax^2 + bx + c = 0, where a, b, and c are real numbers and x is an unknown. The roots of a quadratic equation are the values of x that make the equation true. For example, if we have the equation x^2 - 5x + 6 = 0, then the roots are 3 and 2. A parabola solver can be used to find the roots of any quadratic equation. There are many different types of parabola solvers, but they all work by solving for the values of x that make the equation true. Parabola solvers are essential tools for any mathematician or engineer who needs to solve quadratic equations.
For many centuries, mathematicians have been fascinated by the properties of square roots. These numbers have some unique properties that make them particularly useful for solving certain types of equations. For example, if you take the square root of a negative number, you will end up with an imaginary number. This can be very useful for solving certain types of equations that have no real solution. In addition, square roots can be used to simplify equations that would otherwise be very difficult to solve. For example, if you want to find the value of x that satisfies the equation x^2+2x+1=0, you can use the square root property to simplify the equation and solve it quite easily. As you can see, square roots can be a very powerful tool for solving equations.
How to solve an equation in algebra can be easy once you understand the steps. First, you need to identify the variable. This is the number that you do not know and which will change depending on the value of other numbers in the equation. Second, you need to determine the coefficient. This is the number that is multiplied by the variable. In many equations, the coefficient is simply 1. Third, you need to write down all of the values that are not multiplied by the variable. These are known as constants. Fourth, you need to use algebraic methods to solve for the variable. This usually involves moving all of the terms containing the variable to one side of the equation and all ofthe other terms to the other side. Once you have done this, you can simply solve for the variable by division or multiplication, depending on what type of equation you are dealing with. Finally, you need to check your work by plugging your answer back into the original equation. If everything checks out, thencongratulations-you have just solved an equation!
distance = sqrt((x2-x1)^2 + (y2-y1)^2) When using the distance formula, you are trying to find the length of a line segment between two points. The first step is to identify the coordinates of the two points. Next, plug those coordinates into the distance formula and simplify. The last step is to take the square root of the simplify equation to find the distance. Let's try an example. Find the distance between the points (3,4) and (-1,2). First, we identify the coordinates of our two points. They are (3,4) and (-1,2). Next, we plug those coordinates into our distance formula: distance = sqrt((x2-x1)^2 + (y2-y1)^2)= sqrt((-1-3)^2 + (2-4)^2)= sqrt(16+4)= sqrt(20)= 4.47 Therefore, the distance between the points (3,4) and (-1,2) is 4.47 units.
## More than just an app
It's has helped me a lot on revising math, I don't have to keep approaching other students for help at least I do so once in a while, it's a 100% for me It's funny that I passed math because of this, that's why I'm giving it five stars because it's really helpful
Perla Gray
The Best App ever! If you have some math issue you always can trust in the app, you just take a photo and will be solve in seconds! If they give the explanation without money that will be amazing, but I understand the developers.
Xinia Morris
Math step by step answers Best app to solve geometry problems Solve system of equations matrices How to solve functions Can you solve an expression | 959 | 4,180 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5625 | 5 | CC-MAIN-2023-06 | latest | en | 0.943423 |
https://math.stackexchange.com/questions/1148368/find-the-monic-irreducible-polynomials-of-degree-2-in-f-3 | 1,627,250,015,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046151866.98/warc/CC-MAIN-20210725205752-20210725235752-00109.warc.gz | 402,570,803 | 37,690 | # Find the monic irreducible polynomials of degree 2 in $F_3$
I know that there are 9 distinct monic polynomials of degree 2 in $F_3$. To find which are irreducible, should I just list them all out and check each one, or is there a better way of checking this?
A polynomial of degree $2$ is irreducible if and only if it has not roots in $\mathbf{F}_3$, which is equivalent to say that its discriminant is not a square in $\mathbf{F}_3$. Note $X^2 - s X + p$ your monic polynomial, so that its discriminant, $\Delta = s^2 - p$, must be equal to the only element of $\mathbf{F}_3$ which is not a square, that is $2$. Can you finish by solving $s^2 - p = 2$ in $\mathbf{F}_3^2$ ?
• Also, isn't the discriminant $s^2 - 4p$? – jstnchng Feb 15 '15 at 4:58
• $s$ and $p$ are the coefficients of your monic polynomial with coefficients in $\mathbf{F}_3$, so that the are in $\mathbf{F}_3$ indeed. The discriminant is $s^2 - 4p$ indeed, but remember that in $\mathbf{F}_3$, as $3 = 0$, you have that $-4 = -1$. – Olórin Feb 15 '15 at 10:46
Another way to do this is to think of what the quadratic irrationalities look like over $\Bbb F_3$. You can write them down: $\pm i$, $1\pm i$, and $-1\pm i$, where by $i$ I mean a square root of $-1=2$ in the extended field $\Bbb F_9$. Each conjugate pair that I’ve written gives you a monic quadratic irreducible. This is very constructive, as you see.
• Aren't there three of these though? I did them by hand and found $x^2+1$, $x^2+2$, $x^2+x+2$. How exactly do these pair up? – jstnchng Feb 15 '15 at 4:56
• Right: for instance the pair $1\pm i$ gives you the polynomial $(x-(1+i))(x-(1-i))=x^2+x+2$. – Lubin Feb 15 '15 at 20:43 | 558 | 1,667 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.9375 | 4 | CC-MAIN-2021-31 | latest | en | 0.915561 |
https://intellipaat.com/community/12978/how-do-i-sort-one-vector-based-on-values-of-another | 1,718,450,617,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861586.40/warc/CC-MAIN-20240615093342-20240615123342-00532.warc.gz | 277,945,875 | 23,720 | 2 views
edited
I have a vector x, that I would like to sort based on the order of values in vector y. The two vectors are not of the same length.
x <- c(2, 2, 3, 4, 1, 4, 4, 3, 3)
y <- c(4, 2, 1, 3)
The expected result would be:
[1] 4 4 4 2 2 1 3 3 3
edited by
To sort one vector based on values of another vector, you can use the match() and order() function from the base package as follows:
x <- c(2, 2, 3, 4, 1, 4, 4, 3, 3)
y <- c(4, 2, 1, 3)
match(x,y)
[1] 2 2 4 1 3 1 1 4 4 #returns the relative position of the elements from x to y.
order(match(x,y))
[1] 4 6 7 1 2 5 3 8 9 #orders the indices in arranging order.
x[order(match(x,y))]
[1] 4 4 4 2 2 1 3 3 3 #sorts elements of x based on y.
A one-line form:
x[order(match(x,y))]
[1] 4 4 4 2 2 1 3 3 3 | 332 | 774 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.828125 | 3 | CC-MAIN-2024-26 | longest | en | 0.821051 |
https://doc.sagemath.org/html/en/reference/discrete_geometry/sage/geometry/integral_points.html | 1,669,937,459,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710870.69/warc/CC-MAIN-20221201221914-20221202011914-00873.warc.gz | 253,506,884 | 13,500 | # Cython helper methods to compute integral points in polyhedra.#
class sage.geometry.integral_points.InequalityCollection#
Bases: object
A collection of inequalities.
INPUT:
• polyhedron – a polyhedron defining the inequalities.
• permutation – list; a 0-based permutation of the coordinates. Will be used to permute the coordinates of the inequality.
• box_min, box_max – the (not permuted) minimal and maximal coordinates of the bounding box. Used for bounds checking.
EXAMPLES:
sage: from sage.geometry.integral_points import InequalityCollection
sage: P_QQ = Polyhedron(identity_matrix(3).columns() + [(-2, -1,-1)], base_ring=QQ)
sage: ieq = InequalityCollection(P_QQ, [0,1,2], [0]*3,[1]*3); ieq
The collection of inequalities
integer: (3, -2, -2) x + 2 >= 0
integer: (-1, 4, -1) x + 1 >= 0
integer: (-1, -1, 4) x + 1 >= 0
integer: (-1, -1, -1) x + 1 >= 0
sage: P_RR = Polyhedron(identity_matrix(2).columns() + [(-2.7, -1)], base_ring=RDF)
sage: InequalityCollection(P_RR, [0,1], [0]*2, [1]*2)
The collection of inequalities
integer: (-1, -1) x + 1 >= 0
generic: (-1.0, 3.7) x + 1.0 >= 0
generic: (1.0, -1.35) x + 1.35 >= 0
sage: line = Polyhedron(eqns=[(2,3,7)])
sage: InequalityCollection(line, [0,1], [0]*2, [1]*2 )
The collection of inequalities
integer: (3, 7) x + 2 >= 0
integer: (-3, -7) x + -2 >= 0
are_satisfied(inner_loop_variable)#
Return whether all inequalities are satisfied.
You must call prepare_inner_loop() before calling this method.
INPUT:
• inner_loop_variable – Integer. the 0-th coordinate of the lattice point.
OUTPUT:
Boolean. Whether the lattice point is in the polyhedron.
EXAMPLES:
sage: from sage.geometry.integral_points import InequalityCollection
sage: line = Polyhedron(eqns=[(2,3,7)])
sage: ieq = InequalityCollection(line, [0,1], [0]*2, [1]*2 )
sage: ieq.prepare_next_to_inner_loop([3,4])
sage: ieq.prepare_inner_loop([3,4])
sage: ieq.are_satisfied(3)
False
prepare_inner_loop(p)#
Peel off the inner loop.
In the inner loop of rectangular_box_points(), we have to repeatedly evaluate $$A x+b\geq 0$$. To speed up computation, we pre-evaluate
$c = A x - A_0 x_0 +b = b + \sum_{i=1} A_i x_i$
and only test $$A_0 x_0 +c \geq 0$$ in the inner loop.
You must call prepare_next_to_inner_loop() before calling this method.
INPUT:
• p – the coordinates of the point to loop over. Only the p[1:] entries are used.
EXAMPLES:
sage: from sage.geometry.integral_points import InequalityCollection, print_cache
sage: P = Polyhedron(ieqs=[(2,3,7,11)])
sage: ieq = InequalityCollection(P, [0,1,2], [0]*3,[1]*3); ieq
The collection of inequalities
integer: (3, 7, 11) x + 2 >= 0
sage: ieq.prepare_next_to_inner_loop([2,1,3])
sage: ieq.prepare_inner_loop([2,1,3])
sage: print_cache(ieq)
Cached inner loop: 3 * x_0 + 42 >= 0
Cached next-to-inner loop: 3 * x_0 + 7 * x_1 + 35 >= 0
prepare_next_to_inner_loop(p)#
Peel off the next-to-inner loop.
In the next-to-inner loop of rectangular_box_points(), we have to repeatedly evaluate $$A x-A_0 x_0+b$$. To speed up computation, we pre-evaluate
$c = b + \sum_{i=2} A_i x_i$
and only compute $$A x-A_0 x_0+b = A_1 x_1 +c \geq 0$$ in the next-to-inner loop.
INPUT:
• p – the point coordinates. Only p[2:] coordinates are potentially used by this method.
EXAMPLES:
sage: from sage.geometry.integral_points import InequalityCollection, print_cache
sage: P = Polyhedron(ieqs=[(2,3,7,11)])
sage: ieq = InequalityCollection(P, [0,1,2], [0]*3,[1]*3); ieq
The collection of inequalities
integer: (3, 7, 11) x + 2 >= 0
sage: ieq.prepare_next_to_inner_loop([2,1,3])
sage: ieq.prepare_inner_loop([2,1,3])
sage: print_cache(ieq)
Cached inner loop: 3 * x_0 + 42 >= 0
Cached next-to-inner loop: 3 * x_0 + 7 * x_1 + 35 >= 0
satisfied_as_equalities(inner_loop_variable)#
Return the inequalities (by their index) that are satisfied as equalities.
INPUT:
• inner_loop_variable – Integer. the 0-th coordinate of the lattice point.
OUTPUT:
A set of integers in ascending order. Each integer is the index of a H-representation object of the polyhedron (either a inequality or an equation).
EXAMPLES:
sage: from sage.geometry.integral_points import InequalityCollection
sage: ieqs = InequalityCollection(quadrant, [0,1], [-1]*2, [1]*2 )
sage: ieqs.prepare_next_to_inner_loop([-1,0])
sage: ieqs.prepare_inner_loop([-1,0])
sage: ieqs.satisfied_as_equalities(-1)
frozenset({1})
sage: ieqs.satisfied_as_equalities(0)
frozenset({0, 1})
sage: ieqs.satisfied_as_equalities(1)
frozenset({1})
swap_ineq_to_front(i)#
Swap the i-th entry of the list to the front of the list of inequalities.
INPUT:
EXAMPLES:
sage: from sage.geometry.integral_points import InequalityCollection
sage: P_QQ = Polyhedron(identity_matrix(3).columns() + [(-2, -1,-1)], base_ring=QQ)
sage: iec = InequalityCollection(P_QQ, [0,1,2], [0]*3,[1]*3)
sage: iec
The collection of inequalities
integer: (3, -2, -2) x + 2 >= 0
integer: (-1, 4, -1) x + 1 >= 0
integer: (-1, -1, 4) x + 1 >= 0
integer: (-1, -1, -1) x + 1 >= 0
sage: iec.swap_ineq_to_front(3)
sage: iec
The collection of inequalities
integer: (-1, -1, -1) x + 1 >= 0
integer: (3, -2, -2) x + 2 >= 0
integer: (-1, 4, -1) x + 1 >= 0
integer: (-1, -1, 4) x + 1 >= 0
class sage.geometry.integral_points.Inequality_generic#
Bases: object
An inequality whose coefficients are arbitrary Python/Sage objects
INPUT:
• A – list of coefficients
• b – element
OUTPUT:
Inequality $$A x + b \geq 0$$.
EXAMPLES:
sage: from sage.geometry.integral_points import Inequality_generic
sage: Inequality_generic([2*pi,sqrt(3),7/2], -5.5)
generic: (2*pi, sqrt(3), 7/2) x + -5.50000000000000 >= 0
class sage.geometry.integral_points.Inequality_int#
Bases: object
Fast version of inequality in the case that all coefficients fit into machine ints.
INPUT:
• A – list of integers
• b – integer
• max_abs_coordinates – the maximum of the coordinates that one wants to evaluate the coordinates on; used for overflow checking
OUTPUT:
Inequality $$A x + b \geq 0$$. A OverflowError is raised if a machine integer is not long enough to hold the results. A ValueError is raised if some of the input is not integral.
EXAMPLES:
sage: from sage.geometry.integral_points import Inequality_int
sage: Inequality_int([2,3,7], -5, [10]*3)
integer: (2, 3, 7) x + -5 >= 0
sage: Inequality_int([1]*21, -5, [10]*21)
Traceback (most recent call last):
...
OverflowError: Dimension limit exceeded.
sage: Inequality_int([2,3/2,7], -5, [10]*3)
Traceback (most recent call last):
...
ValueError: Not integral.
sage: Inequality_int([2,3,7], -5.2, [10]*3)
Traceback (most recent call last):
...
ValueError: Not integral.
sage: Inequality_int([2,3,7], -5*10^50, [10]*3) # actual error message can differ between 32 and 64 bit
Traceback (most recent call last):
...
OverflowError: ...
sage.geometry.integral_points.loop_over_parallelotope_points(e, d, VDinv, R, lattice, A=None, b=None)#
The inner loop of parallelotope_points().
INPUT:
See parallelotope_points() for e, d, VDinv, R, lattice.
• A, b: Either both None or a vector and number. If present, only the parallelotope points satisfying $$A x \leq b$$ are returned.
OUTPUT:
The points of the half-open parallelotope as a tuple of lattice points.
EXAMPLES:
sage: e = [3]
sage: d = prod(e)
sage: VDinv = matrix(ZZ, [[1]])
sage: R = column_matrix(ZZ,[3,3,3])
sage: lattice = ZZ^3
sage: from sage.geometry.integral_points import loop_over_parallelotope_points
sage: loop_over_parallelotope_points(e, d, VDinv, R, lattice)
((0, 0, 0), (1, 1, 1), (2, 2, 2))
sage: A = vector(ZZ, [1,0,0])
sage: b = 1
sage: loop_over_parallelotope_points(e, d, VDinv, R, lattice, A, b)
((0, 0, 0), (1, 1, 1))
sage.geometry.integral_points.parallelotope_points(spanning_points, lattice)#
Return integral points in the parallelotope starting at the origin and spanned by the spanning_points.
See semigroup_generators() for a description of the algorithm.
INPUT:
• spanning_points – a non-empty list of linearly independent rays ($$\ZZ$$-vectors or toric lattice elements), not necessarily primitive lattice points.
OUTPUT:
The tuple of all lattice points in the half-open parallelotope spanned by the rays $$r_i$$,
$\mathop{par}(\{r_i\}) = \sum_{0\leq a_i < 1} a_i r_i$
By half-open parallelotope, we mean that the points in the facets not meeting the origin are omitted.
EXAMPLES:
Note how the points on the outward-facing factes are omitted:
sage: from sage.geometry.integral_points import parallelotope_points
sage: rays = list(map(vector, [(2,0), (0,2)]))
sage: parallelotope_points(rays, ZZ^2)
((0, 0), (0, 1), (1, 0), (1, 1))
The rays can also be toric lattice points:
sage: rays = list(map(ToricLattice(2), [(2,0), (0,2)]))
sage: parallelotope_points(rays, ToricLattice(2))
(N(0, 0), N(0, 1), N(1, 0), N(1, 1))
A non-smooth cone:
sage: c = Cone([ (1,0), (1,2) ])
sage: parallelotope_points(c.rays(), c.lattice())
(N(0, 0), N(1, 1))
A ValueError is raised if the spanning_points are not linearly independent:
sage: rays = list(map(ToricLattice(2), [(1,1)]*2))
sage: parallelotope_points(rays, ToricLattice(2))
Traceback (most recent call last):
...
ValueError: The spanning points are not linearly independent!
sage.geometry.integral_points.print_cache(inequality_collection)#
Print the cached values in Inequality_int (for debugging/doctesting only).
EXAMPLES:
sage: from sage.geometry.integral_points import InequalityCollection, print_cache
sage: P = Polyhedron(ieqs=[(2,3,7)])
sage: ieq = InequalityCollection(P, [0,1], [0]*2,[1]*2); ieq
The collection of inequalities
integer: (3, 7) x + 2 >= 0
sage: ieq.prepare_next_to_inner_loop([3,5])
sage: ieq.prepare_inner_loop([3,5])
sage: print_cache(ieq)
Cached inner loop: 3 * x_0 + 37 >= 0
Cached next-to-inner loop: 3 * x_0 + 7 * x_1 + 2 >= 0
sage.geometry.integral_points.ray_matrix_normal_form(R)#
Compute the Smith normal form of the ray matrix for parallelotope_points().
INPUT:
• R$$\ZZ$$-matrix whose columns are the rays spanning the parallelotope.
OUTPUT:
A tuple containing e, d, and VDinv.
EXAMPLES:
sage: from sage.geometry.integral_points import ray_matrix_normal_form
sage: R = column_matrix(ZZ,[3,3,3])
sage: ray_matrix_normal_form(R)
([3], 3, [1])
sage.geometry.integral_points.rectangular_box_points(box_min, box_max, polyhedron=None, count_only=False, return_saturated=False)#
Return the integral points in the lattice bounding box that are also contained in the given polyhedron.
INPUT:
• box_min – A list of integers. The minimal value for each coordinate of the rectangular bounding box.
• box_max – A list of integers. The maximal value for each coordinate of the rectangular bounding box.
• polyhedron – A Polyhedron_base, a PPL C_Polyhedron, or None (default).
• count_only – Boolean (default: False). Whether to return only the total number of vertices, and not their coordinates. Enabling this option speeds up the enumeration. Cannot be combined with the return_saturated option.
• return_saturated – Boolean (default: False. Whether to also return which inequalities are saturated for each point of the polyhedron. Enabling this slows down the enumeration. Cannot be combined with the count_only option.
OUTPUT:
By default, this function returns a tuple containing the integral points of the rectangular box spanned by box_min and box_max and that lie inside the polyhedron. For sufficiently large bounding boxes, this are all integral points of the polyhedron.
If no polyhedron is specified, all integral points of the rectangular box are returned.
If count_only is specified, only the total number (an integer) of found lattice points is returned.
If return_saturated is enabled, then for each integral point a pair (point, Hrep) is returned where point is the point and Hrep is the set of indices of the H-representation objects that are saturated at the point.
ALGORITHM:
This function implements the naive algorithm towards counting integral points. Given min and max of vertex coordinates, it iterates over all points in the bounding box and checks whether they lie in the polyhedron. The following optimizations are implemented:
• Cython: Use machine integers and optimizing C/C++ compiler where possible, arbitrary precision integers where necessary. Bounds checking, no compile time limits.
• Unwind inner loop (and next-to-inner loop):
$Ax \leq b \quad \Leftrightarrow \quad a_1 x_1 ~\leq~ b - \sum_{i=2}^d a_i x_i$
so we only have to evaluate $$a_1 * x_1$$ in the inner loop.
• Coordinates are permuted to make the longest box edge the inner loop. The inner loop is optimized to run very fast, so its best to do as much work as possible there.
• Continuously reorder inequalities and test the most restrictive inequalities first.
• Use convexity and only find first and last allowed point in the inner loop. The points in-between must be points of the polyhedron, too.
EXAMPLES:
sage: from sage.geometry.integral_points import rectangular_box_points
sage: rectangular_box_points([0,0,0],[1,2,3])
((0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 0, 3),
(0, 1, 0), (0, 1, 1), (0, 1, 2), (0, 1, 3),
(0, 2, 0), (0, 2, 1), (0, 2, 2), (0, 2, 3),
(1, 0, 0), (1, 0, 1), (1, 0, 2), (1, 0, 3),
(1, 1, 0), (1, 1, 1), (1, 1, 2), (1, 1, 3),
(1, 2, 0), (1, 2, 1), (1, 2, 2), (1, 2, 3))
sage: from sage.geometry.integral_points import rectangular_box_points
sage: rectangular_box_points([0,0,0],[1,2,3], count_only=True)
24
sage: cell24 = polytopes.twenty_four_cell()
sage: rectangular_box_points([-1]*4, [1]*4, cell24)
((-1, 0, 0, 0), (0, -1, 0, 0), (0, 0, -1, 0), (0, 0, 0, -1),
(0, 0, 0, 0),
(0, 0, 0, 1), (0, 0, 1, 0), (0, 1, 0, 0), (1, 0, 0, 0))
sage: d = 3
sage: dilated_cell24 = d*cell24
sage: len( rectangular_box_points([-d]*4, [d]*4, dilated_cell24) )
305
sage: d = 6
sage: dilated_cell24 = d*cell24
sage: len( rectangular_box_points([-d]*4, [d]*4, dilated_cell24) )
3625
sage: rectangular_box_points([-d]*4, [d]*4, dilated_cell24, count_only=True)
3625
sage: polytope = Polyhedron([(-4,-3,-2,-1),(3,1,1,1),(1,2,1,1),(1,1,3,0),(1,3,2,4)])
sage: pts = rectangular_box_points([-4]*4, [4]*4, polytope); pts
((-4, -3, -2, -1), (-1, 0, 0, 1), (0, 1, 1, 1), (1, 1, 1, 1), (1, 1, 3, 0),
(1, 2, 1, 1), (1, 2, 2, 2), (1, 3, 2, 4), (2, 1, 1, 1), (3, 1, 1, 1))
sage: all(polytope.contains(p) for p in pts)
True
sage: set(map(tuple,pts)) == \
....: set([(-4,-3,-2,-1),(3,1,1,1),(1,2,1,1),(1,1,3,0),(1,3,2,4),
....: (0,1,1,1),(1,2,2,2),(-1,0,0,1),(1,1,1,1),(2,1,1,1)]) # computed with PALP
True
Long ints and non-integral polyhedra are explicitly allowed:
sage: polytope = Polyhedron([[1], [10*pi.n()]], base_ring=RDF)
sage: len( rectangular_box_points([-100], [100], polytope) )
31
sage: halfplane = Polyhedron(ieqs=[(-1,1,0)])
sage: rectangular_box_points([0,-1+10^50], [0,1+10^50])
((0, 99999999999999999999999999999999999999999999999999),
(0, 100000000000000000000000000000000000000000000000000),
(0, 100000000000000000000000000000000000000000000000001))
sage: len( rectangular_box_points([0,-100+10^50], [1,100+10^50], halfplane) )
201
Using a PPL polyhedron:
sage: from ppl import Variable, Generator_System, C_Polyhedron, point
sage: gs = Generator_System()
sage: x = Variable(0); y = Variable(1); z = Variable(2)
sage: gs.insert(point(0*x + 1*y + 0*z))
sage: gs.insert(point(0*x + 1*y + 3*z))
sage: gs.insert(point(3*x + 1*y + 0*z))
sage: gs.insert(point(3*x + 1*y + 3*z))
sage: poly = C_Polyhedron(gs)
sage: rectangular_box_points([0]*3, [3]*3, poly)
((0, 1, 0), (0, 1, 1), (0, 1, 2), (0, 1, 3), (1, 1, 0), (1, 1, 1), (1, 1, 2), (1, 1, 3),
(2, 1, 0), (2, 1, 1), (2, 1, 2), (2, 1, 3), (3, 1, 0), (3, 1, 1), (3, 1, 2), (3, 1, 3))
Optionally, return the information about the saturated inequalities as well:
sage: cube = polytopes.cube()
sage: cube.Hrepresentation(0)
An inequality (-1, 0, 0) x + 1 >= 0
sage: cube.Hrepresentation(1)
An inequality (0, -1, 0) x + 1 >= 0
sage: cube.Hrepresentation(2)
An inequality (0, 0, -1) x + 1 >= 0
sage: rectangular_box_points([0]*3, [1]*3, cube, return_saturated=True)
(((0, 0, 0), frozenset()),
((0, 0, 1), frozenset({2})),
((0, 1, 0), frozenset({1})),
((0, 1, 1), frozenset({1, 2})),
((1, 0, 0), frozenset({0})),
((1, 0, 1), frozenset({0, 2})),
((1, 1, 0), frozenset({0, 1})),
((1, 1, 1), frozenset({0, 1, 2})))
sage.geometry.integral_points.simplex_points(vertices)#
Return the integral points in a lattice simplex.
INPUT:
• vertices – an iterable of integer coordinate vectors. The indices of vertices that span the simplex under consideration.
OUTPUT:
A tuple containing the integral point coordinates as $$\ZZ$$-vectors.
EXAMPLES:
sage: from sage.geometry.integral_points import simplex_points
sage: simplex_points([(1,2,3), (2,3,7), (-2,-3,-11)])
((-2, -3, -11), (0, 0, -2), (1, 2, 3), (2, 3, 7))
The simplex need not be full-dimensional:
sage: simplex = Polyhedron([(1,2,3,5), (2,3,7,5), (-2,-3,-11,5)])
sage: simplex_points(simplex.Vrepresentation())
((2, 3, 7, 5), (0, 0, -2, 5), (-2, -3, -11, 5), (1, 2, 3, 5))
sage: simplex_points([(2,3,7)])
((2, 3, 7),) | 5,663 | 16,998 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.09375 | 3 | CC-MAIN-2022-49 | longest | en | 0.579042 |
http://www.surveymonkey.com/s/F37L5GS | 1,369,303,550,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368703227943/warc/CC-MAIN-20130516112027-00048-ip-10-60-113-184.ec2.internal.warc.gz | 743,279,722 | 5,687 | # Are Your Friends Making You Broke?Exit this survey
1. You are:
You are: MaleFemale
2. How old are you?
How old are you? 17 and under18-2425-3435 and over
3. In an average year, how much do you think you spend on friends’ weddings/showers/bachelorettes (including gifts, travel, and, if you were a bridesmaid, average in expenses like dresses and shoes)
In an average year, how much do you think you spend on friends’ weddings/showers/bachelorettes (including gifts, travel, and, if you were a bridesmaid, average in expenses like dresses and shoes) Under \$200\$200-\$500Between \$500-\$1000\$1,000-\$2,000\$2,000 or more
4. How much do you generally spend on a birthday present for your BFF?
How much do you generally spend on a birthday present for your BFF? Nothing—we don’t do presents\$50 or less\$50-\$100\$100 or more
5. Each year, about how much do you spend on all your other friend’s birthday presents combined (including chipping in for her birthday dinner and/or drinks)
Each year, about how much do you spend on all your other friend’s birthday presents combined (including chipping in for her birthday dinner and/or drinks) Nada\$100 or less\$100 to \$200\$200 or more
6. In the past year, how much money did you end up donating to friends who were doing an event (Run for Cancer, Bike for Diabetes, etc) for charity?
In the past year, how much money did you end up donating to friends who were doing an event (Run for Cancer, Bike for Diabetes, etc) for charity? \$50 or less\$50-\$100\$100-\$200\$200 or more
7. How much money have you spent on baby gifts for friends in the past year?
How much money have you spent on baby gifts for friends in the past year? NoneUnder \$50\$50 to \$100\$100 or more
8. About how many times a month do you head to a friend’s casa for dinner, a party, or a tv-watching date and bring a bottle of vino?
About how many times a month do you head to a friend’s casa for dinner, a party, or a tv-watching date and bring a bottle of vino? 1 or lessMaybe 23 or 4More than 4
9. How much cash do you think you spend in a month randomly picking up the tab at a happy hour or drinks?
How much cash do you think you spend in a month randomly picking up the tab at a happy hour or drinks? Under \$25\$25 to \$50\$50 to \$100\$100 or more
10. How much would you say you spend in a year on random pick-me-up gifts (flowers, lip gloss, a magazine or book, etc) for friends going through a tough time like a breakup or job loss?
How much would you say you spend in a year on random pick-me-up gifts (flowers, lip gloss, a magazine or book, etc) for friends going through a tough time like a breakup or job loss? Under \$25\$25-\$50\$50-\$100\$100 or more
11. How often would you say you lend a friend a few bucks because they’re short on their part of the tab, or they just need to buy that killer pair of shoes—and never get it back?
How often would you say you lend a friend a few bucks because they’re short on their part of the tab, or they just need to buy that killer pair of shoes—and never get it back? Maybe a few times a yearProbably about once a monthA couple of times a monthPretty much weekly
12. When you do lend money, how much would you say you lose each time?
When you do lend money, how much would you say you lose each time? None, I don’t lend money or if I do, my friends pay me backUnder \$10Between \$10 and \$20Between \$20 and \$50 | 881 | 3,426 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2013-20 | latest | en | 0.940879 |
https://www.doorsteptutor.com/Exams/ISS/Paper-1-MCQ/Questions/Part-27.html | 1,618,175,107,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038065492.15/warc/CC-MAIN-20210411204008-20210411234008-00085.warc.gz | 819,656,597 | 6,855 | # ISS (Statistical Services) Statistics Paper I (New 2016 MCQ Pattern): Questions 134 - 138 of 472
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## Question 134
### Question
MCQ▾
What is the output of this C code?
1. `void main()`
2. `{`
3. ` int x=1;`
4. ` if (x < 2)`
5. ` main();`
6. `}`
### Choices
Choice (4)Response
a.
Infinite calls to main
b.
Run time error
c.
Compilation error
d.
Main is called twice
## Question 135
### Question
MCQ▾
Which of the following is not a pointer declaration?
### Choices
Choice (4)Response
a.
double B [] = { ‘25’ , ‘36’ , ‘11’ } ;
b.
double A [20] ;
c.
char ptr;
d.
double ptr;
## Question 136
### Question
MCQ▾
Point out the error, if any in the program.
1. `#include<stdio.h>`
2. `int main()`
3. `{`
4. ` int x = 1;`
5. ` switch(x)`
6. ` {`
7. ` }`
8. ` printf("Hello");`
9. ` return 0;`
10. `}`
### Choices
Choice (4)Response
a.
No Error
b.
Error: No case statement specified
c.
Error: No default specified
d.
Error: infinite loop occurs
## Question 137
### Question
MCQ▾
What is the output of this C code?
1. `#include <stdio.h>`
2. `int main()`
3. `{`
4. ` int x = 2;`
5. ` int y= x +(x== 10);`
6. ` printf("%dn", y);`
7. `}`
### Choices
Choice (4)Response
a.
4
b.
2
c.
20
d.
Question does not provide sufficient data or is vague
## Question 138
### Question
MCQ▾
Which of the following statement is correct regarding the following program?
1. `int main( )`
2. `{`
3. ` const double PI;`
4. ` int n;`
5. ` PI = 3.14159265358979;`
6. ` n = 22;`
7. `}`
### Choices
Choice (4)Response
a.
Const declared PI must be initialized at the time of declaration.
b.
Initialization of int n is incorrect.
c.
None of the above
d.
Question does not provide sufficient data or is vague | 725 | 2,147 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2021-17 | latest | en | 0.532607 |
https://www.study-tutor.com/2019/12/atomic-radius.html | 1,601,492,692,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600402127397.84/warc/CC-MAIN-20200930172714-20200930202714-00315.warc.gz | 992,469,294 | 21,389 | Friday, 6 December 2019
Atomic Radius - The general picture of an atom in our mind is that of a sphere. If it is regarded as correct, then its definition is given below.
https://www.universetoday.com/
The distance between the center of its nucleus and electrons in the last orbit.
-OR -
It is defined as the distance between the nucleus and the outermost orbit.
However, remember according to quantum theory, there is no certainty about the exact position of electrons at any time. Theoretically, an electron, at one time, maybe very close to the nucleus while at other times it may be far away from the nucleus. Also, It is not possible to measure the exact value of the atomic radius of an atom of the element because an atom is very much smaller in size.
So, on certain facts, it is difficult to explain the exact atomic radius definition. Let’s explain it more clearly.
Why not possible to exact determination of Atomic Radius?
A. It is not possible to isolate a single atom.
B. It is not possible to measure the exact distance of the atom does not have a well-defined shape or boundary and the probability of electron is level zero even at a large distance from the nucleus.
C. It is likely to change due to environmental effect and many more reasons.
However, we can express the different forms of atom depending upon the nature of the bonding of atoms. In spite of the above limitations, There are three operational concepts:
• If the bonding is covalent, the radius is called a covalent radius.
• If the bonding is ionic, the radius is called the ionic radius.
• If the two atoms are not bonded by a chemical bond (as in noble gases) the radius is called van der Waal’s radius.
The are three types of atomic radius.
Covalent radius: If bonding present in between atoms in a molecule is covalent, the radius is called covalent radius. It is half of the distance between the nucleus of two like atoms bonded together by a single bond or by a covalent bond.
If the two atoms linked to each other by a double bond or triple Bond, then the half of the Internuclear distance does not represent the covalent radius.
Metallic radius: It is defined as one half of the inter nuclear distance between the nucleus of two adjacent atoms in the metallic lattice. The metallic radius of an element is greater than the covalent radius.
Since the metallic bond is weaker than the covalent bond the internuclear molecular distance between the two atoms in the metallic bond is more than the covalent bond.
• The metallic bond is more than the covalent bond
Van der Waal’s radius: It is one half of the distance between the nucleus of two adjacent atoms belonging to two neighboring molecules of an element in the solid state.
Actually, the van der Waal forces are weak forces their magnitude(power) of attraction is smaller in gaseous as well as in the liquid state of the substance. Therefore radius is determined in the solid-state when the magnitude of the force is expected to a maximum.
During the research, scientists found the smallest particle of matter and named it as an atom. The different atoms of different elements show different chemical and physical properties. This can be seen when the atomic radius change in periodic table trend. The change in the atomic radii has a great impact on the behavior of atoms during the chemical reaction. It is because it influences the ionization energy, chemical reactivity, electronegativity and many other factors.
https://www.ibchem.com
It is to be noted that the atomic radius of the last element in each period which is a noble gas element is quite large. It is because noble gases are considered van der Waal’s radius which always has the higher value than a covalent radius. When we compare the three atomic radii the order of forces is
In a period, the number of shells remains the same but the nuclear charge increases. This resulting increase in the force of attraction towards the nucleus, which causes contraction of size.
• Nuclear attraction ∝ 1 / Atomic Radii.
• Principal quantum number(n) ∝ Atomic radii.
• Screening effect ∝ Atomic Radii.
• The number of bond ∝ 1 / Atomic Radii.
In a group, as we move from top to bottom in a group the atomic radius increases with the increase of atomic number, this is due to the fact that the number of energy shells increases.
• The size of Hydrogen is the smallest.
• Francium having atomic number 87 has a larger covalent and Van Der Waals radius than Cesium.
• Since Francium is an extremely unstable element. So, Caesium has the largest atomic number.
Atomic Radius Trend in Period and Groups
Period
Along a period, the atomic radius trend (or radii) of the elements generally decrease from left to right. The atomic radii of the elements present in the second period are given.
Element Li Be B C N O Nuclear Charge +3 +4 +5 +6 +7 +8 Atomic Radius (pm) 152 111 88 77 75 74
From the values, it is clear that the alkali metal (Li) placed on the extreme left has the maximum atomic radius while the halogen (F) on the extreme right has the minimum value.
Explanation
In moving from left to right in a period,
The nuclear charge gradually increases by one unit and at the same time, one electron is also being added to the electron shell. Due to increased nuclear charge from left to the right, the electrons are also getting attracted more and more towards the nucleus. Consequently, the atomic size is expected to decrease as shown in the case of the elements of the second period.
It may be noted that the atomic radius of the last element in each period which is a noble gas element is quite large. For example, in the second period, the atomic radius of neon (Ne) is 160 pm (not shown). Actually, it is van der Waals radius while the rest of the elements have covalent radii. Therefore, no comparison can be made. The van der Waals radii also decrease in a period from left to the right.
Group
The atomic radii of the elements in every group of the periodic table increase as we move downwards. Covalent Radii of the alkali metals present in group 1 are given. Since all of them are metallic in nature, their metallic radii have also been given for reference.
Element Li Na K Rb Cs Fr Nuclear Charge +3 +11 +19 +37 +55 +87 Covalent Radius (pm) 123 157 202 216 235 – Metallic Radius (pm) 125 186 231 244 262 –
From the values, it is quite clear that the atomic radius of lithium (Li) is the minimum while that of caesium (Cs) is the maximum. The value of the last element francium (Fr) is not known since being as radioactive in nature, it is unstable.
Explanation
On moving down a group, there is an increase in the principal quantum number and thus, an increase in the number of electron shells. Therefore, the atomic size is expected to increase. But at the same time, there is an increase in the atomic number or nuclear charge also. As a result. the atomic size must decrease. However, the effect of an increase in the electron shells is more pronounced than the effect of an increase in nuclear charge. Consequently, the atomic size or atomic radius increases down a group. This is well supported by alkali metals of group 1 the values given in Table for the alkali metals. | 1,586 | 7,214 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2020-40 | latest | en | 0.950309 |
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# Read : Ch. 12 in Electric Circuits, 9 th Edition by Nilsson - PowerPoint PPT Presentation
Chapter 12 EGR 272 – Circuit Theory II. 1. Read : Ch. 12 in Electric Circuits, 9 th Edition by Nilsson Handout : Laplace Transform Properties and Common Laplace Transforms. Laplace Transforms – an extremely important topic in EE! Key Uses of Laplace Transforms :
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Chapter 12 EGR 272 – Circuit Theory II
1
Read: Ch. 12 in Electric Circuits, 9th Edition by Nilsson
Handout: Laplace Transform Properties and Common Laplace Transforms
• Laplace Transforms – an extremely important topic in EE!
• Key Uses of Laplace Transforms:
• Solving differential equations
• Analyzing circuits in the s-domain
• Transfer functions
• Frequency response
• Applications in many courses
• Testing:
• Some calculators can often be used to find Laplace transforms and inverse Laplace transforms. However, it is also easy to make mistakes with the calculators and if the student is not familiar with the material, the mistakes might easily go undetected. As a result:
• Courses Using Laplace Transforms:
• Circuit Theory II
• Electronics
• Control Theory
• Discrete Time Systems (z-transforms)
• Communications
• Others
No calculators allowed on Test #3
Chapter 12 EGR 272 – Circuit Theory II
Chapter 12 EGR 272 – Circuit Theory II
2
2
Notation:
F(s) = L{f(t)} = the Laplace transform of f(t).
f(t) = L-1{F(s)} = the inverse Laplace transform of F(s).
Uniqueness: Every f(t) has a unique F(s) and every F(s) has a unique f(t).
L
f(t)
F(s)
L-1
Note:
Transferring to the s-domain when using Laplace transforms is similar to transferring to the phasor domain for AC circuit analysis.
Chapter 12 EGR 272 – Circuit Theory II
3
jw
s-plane
Definition:
(one-sided Laplace transform)
where
s = + jw = complex frequency
= Re[s] and w = Im[s]
sometimes complex frequency values are displayed on the s-plane as follows:
Note: The s-plane is sometimes used to plot the roots of systems, determine system stability, and more. It is used routinely in later courses, such as Control Theory.
Chapter 12 EGR 272 – Circuit Theory II
4
Convergence: A negative exponent (real part) is required within the integral definition of the Laplace Transform for it to converge, so Laplace Transforms are often defined over a specific range (such as for > 0). Convergence will discussed in the first couple of examples in this course to illustrate the point, but will not be stressed afterwards as convergence is not typically a problem in circuits problems.
Determining Laplace Transforms - Laplace transforms can be found by:
1) Definition - use the integral definition of the Laplace transform
2) Tables - tables of Laplace transforms are common in engineering and math texts. The table on the following page will be provided on tests.
3) Using properties of Laplace transforms - if the Laplace transforms of a few basic functions are known, properties of Laplace transforms can be used to find the Laplace transforms of more complex functions.
Chapter 12 EGR 272 – Circuit Theory II
5
Table of Laplace Transforms(to be provided on tests)
Chapter 12 EGR 272 – Circuit Theory II
6
Example: If f(t) = u(t), find F(s) using the definition of the Laplace transform. List the range over which the transform is defined (converges).
Example: If f(t) = e-at u(t),find F(s) using the definition of the Laplace transform. List the range over which the transform is defined (converges).
Chapter 12 EGR 272 – Circuit Theory II
7
Example: Find F(s) if f(t) = cos(wot)u(t)
(Hint: use Euler’s Identity)
Example: Find F(s) if f(t) = sin(wot)u(t)
Chapter 12 EGR 272 – Circuit Theory II
8
Laplace Transform Properties
Laplace transforms of complicated functions may be found by using known transforms of simple functions and then by applying properties in order to see the effect on the Laplace transform due to some modification to the time function. Ten properties will be discussed as shown below.
Table of Laplace Transform Properties (will be provided on tests)
Chapter 12 EGR 272 – Circuit Theory II
9
Laplace Transform Properties:
1. Linearity:
L {af(t)} = aF(s)
L {f1(t) + f2(t) } = F1(s) + F2(s)
2. Superposition:
Example: Use the results of the last two examples plus the two properties above to find F(s) if f(t) = 25(1 – e-3t )u(t)
Chapter 12 EGR 272 – Circuit Theory II
10
This means that if you know F(s) for any f(t), then the result of multiplying f(t) by e-at is that you replace each s in F(s) by s+a.
Laplace Transform Properties: (continued)
3. Modulation:
L {e-atf(t)} = F(s + a)
Example: Find V(s) if v(t) = 10e-2tcos(3t)u(t)
This solution shows a good way to use Laplace transform properties:
Begin with a known transform
Apply property
Apply property
Etc
Chapter 12 EGR 272 – Circuit Theory II
11
Example: Find I(s) if i(t) = 4e-20t sin(7t)u(t)
Chapter 12 EGR 272 – Circuit Theory II
12
Laplace Transform Properties: (continued)
4. Time-Shifting:
Note: Be sure that allt’s are in the (t -) form when using this property.
L {f(t - )u(t - )} = e-sF(s)
Example: Find L {4e-2(t - 3) u(t - 3)}
Example: Find L {10e-2(t - 4)sin(4[t - 4])u(t - 4)}
Chapter 12 EGR 272 – Circuit Theory II
13
Note: Properties can sometimes be applied in different orders. However, one of the methods may be easier. Practice helps in deciding which method to use.
Example: Find F(s) if f(t) = 4e-3t u(t - 5) using 2 approaches:
A) By applying modulation and then time-shifting
B) By applying time-shifting and then modulation
Chapter 12 EGR 272 – Circuit Theory II
14
Example: Find L {4e-3tcos(4[t - 6])u(t - 6)}
Chapter 12 EGR 272 – Circuit Theory II
15
Laplace Transform Properties: (continued)
5. Scaling:
In other words, the result of replacing each (t) in a function with (at) is that each s in the transform is replaced by s/a and the transform is also divided by a.
Note: This is not a commonly used property.
Example: Find F(s) if f(t) = 12cos(3t)u(t)
Chapter 12 EGR 272 – Circuit Theory II
16
Laplace Transform Properties: (continued)
6. Real (Time) Differentiation:
Example: Find L{f ’(t)}
Example: Find L{f ’’(t)}
Example: Find L{f ’’(t)}
Example: Find L{f n(t)}
Chapter 12 EGR 272 – Circuit Theory II
17
Example: Find the Laplace transform of the familiar relationship:
7. Real (Time) Integration:
Example: Find
Chapter 12 EGR 272 – Circuit Theory II
18
Example: Find the Laplace transform of the familiar relationship:
Chapter 12 EGR 272 – Circuit Theory II
19
Laplace Transform Properties: (continued)
8. Complex Differentiation:
Example: Find L {tu(t)}
Example: Find L {t2 u(t)}
Example: Find L {t3 u(t)}
Example: Find L {t n u(t)}
Chapter 12 EGR 272 – Circuit Theory II
20
Example: Find L {3te-2tcos(4t)u(t)}
Example: Find L {tu(t - 2)}
Chapter 12 EGR 272 – Circuit Theory II
21
Note: This is not a commonly used property. Multiplying by t is common (such a with repeated
roots), but dividing by t is rare.
Laplace Transform Properties: (continued)
9. Complex Integration:
Example: Find
Chapter 12 EGR 272 – Circuit Theory II
22
Laplace Transform Properties: (continued)
10. Convolution:
L{f(t) * g(t)} = F(s)·G(s)
f(t) * g(t) reads as “f(t) convolved with g(t)”
Convolution is defined by the difficult integral relationship shown below.
Evaluating this integral is covered in a later course.
Laplace transforms are often used to bypass the convolution integral (illustrated on the following page). Since L{f(t) * g(t)} = F(s) G(s) we can determine f(t)*g(t) using
f(t)*g(t) = L-1{F(s)G(s)}
Chapter 12 EGR 272 – Circuit Theory II
23
The method of using Laplace transforms to bypass the convolution integral is illustrated by the diagram below.
Evaluate
difficult
convolution
integral
f(t)*g(t) = L-1{F(s)G(s)}
Given:
f(t), g(t)
Find:
f(t)*g(t) = ?
Take
Laplace
Transform
Take
Inverse
Laplace
Transform
F(s), G(s)
F(s)·G(s)
Multiply
Chapter 12 EGR 272 – Circuit Theory II
24
Example: If f(t) = 2e-2tu(t) and g(t) = 4e-3tu(t), find f(t)*g(t) using Laplace transforms.
Chapter 12 EGR 272 – Circuit Theory II
25
Impulse Function
(t) = impulse function
The impulse function is defined as:
Delta functions are often illustrated as shown below.
Illustration
To illustrate the concept that the area under (t) = 1 (not the height =1), consider the function f(t) shown below:
Chapter 12 EGR 272 – Circuit Theory II
26
+ v(t) -
i(t)
C
Example:When do impulse functions occur? Consider the example shown below. Sketch the capacitor current.
Chapter 12 EGR 272 – Circuit Theory II
27
Laplace Transform of an impulse function
The Laplace transform of an impulse function can be found using the definition of the Laplace transform:
Since (t) only exits at t=0, e-st only needs to be evaluated at t = 0 (this is sometimes called the sifting property), so:
L {(t)} = 1
so
unctionscan easily be produced by real circuits. Constant terms in F(s) will correspond to impulse functions in f(t). One rule that will be proven next class related to inverse Laplace transforms is that if F(s) = D(s)/N(s), it is required that the order of D(s) be less than the order of N(s) in order to use Partial Factions Expansion (also to be discussed next class).
Chapter 12 EGR 272 – Circuit Theory II
28
Impulse functions can occur in real circuits. Constant terms in F(s) will correspond to impulse functions in f(t). We will soon see that if the order of N(s) is not less than the order of D(s), we should begin by using long division before finding an inverse Laplace transform.
Example: Find f(t) for F(s) shown below. (Hint: Order of N(s) = 2 and order of D(s) = 2, so begin with long division)
Chapter 12 EGR 272 – Circuit Theory II
29
f(t)
f(t)
6
12
t
t
0
2
4
4
0
Laplace Transforms of waveforms
Piecewise-continuous waveforms can be expressed using unit functions. Laplace transforms of these expressions can then be found.
Example: Find F(s) for f(t) shown below.
Example: Find F(s) for f(t) shown below. | 2,984 | 10,869 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2018-43 | latest | en | 0.815413 |
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For technical questions regarding estimation of single equations, systems, VARs, Factor analysis and State Space Models in EViews. General econometric questions and advice should go in the Econometric Discussions forum.
Moderators: EViews Gareth, EViews Moderator
Did you use forum search?
Posts: 1518
Joined: Thu Nov 20, 2008 12:04 pm
Re: HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?
First, declare a coefficient vector that corresponds to non-zero elements of the matrix A and initialize it. In your case, it would be something like the following:
Code: Select all
`coef(6) AmatAmat(1) = .2 'A(2,1)Amat(2) = .2 'A(2,2)Amat(3) = .2 'A(2,3)Amat(4) = .2 'A(3,1)Amat(5) = .2 'A(3,2)Amat(6) = .2 'A(3,3)`
And then, you should modify the equations or series accordingly. For instance, sqres2 and res1res2 should now be defined as:
Code: Select all
`tvgarchm.append sqres2 = (y2-mu(2)-Amat(1)*y1(-1)-Amat(2)*y2(-1)-Amat(3)*y3(-1)-lambda(2)*var_y2)^2tvgarchm.append res1res2 = (y1-0.5*var_y1)*(y2-mu(2)-Amat(1)*y1(-1)-Amat(2)*y2(-1)-Amat(3)*y3(-1)-lambda(2)*var_y2)`
You can modify the code along with these lines...
jpk
Posts: 6
Joined: Tue Aug 16, 2011 4:01 am
Re: HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?
Thank you. When I make these changes and run the program I get an error message: 'missing values in @logl series'. Any tips?
Did you use forum search?
Posts: 1518
Joined: Thu Nov 20, 2008 12:04 pm
Re: HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?
This is quite a common mistake made by users when modeling logl in EViews, so please search the forum for possible remedies...
JackCrow
Posts: 2
Joined: Thu Nov 24, 2011 10:51 pm
Re: HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?
Hello. I have been attempting to use the code presented and discussed in this thread to estimate a bivariate garch-in-mean model. I have three major questions.
1. Is there any way to modify the code to make it constant conditional covariance as opposed to BEKK?
2. What exactly is the current program doing? It seems to be estimating two univariate garch-in-mean series and then using those series to generate logl-maximized coefficients in the bivariate model, but this doesn't get around generated regressors, right?
3. How do I actually interpret results? I'm interested in the role of the conditional variance of each equation in both mean equations, i.e., if you have y1=c(1)*garch1+c(2)*garch2+(stuff), y2=c(3)*garch1+c(4)*garch2+(stuff), I want to estimate c(1) through c(4). I understand that lambda(1) is c(1) and lambda(2) is c(4), but the current program seems to restrict the model to two coefficients, with the off-diagonal element of H (the conditional covariance) replacing garch2 in the first equation and garch1 in the second. Correct? If I am interpreting this right, how do I get c(2) and c(3)?
Thank you very much for your help.
banhong86
Posts: 2
Joined: Mon Mar 11, 2013 4:05 pm
Re: HOW TO ESTIMATE A GARCH (1,1) (2,2) (1,2) (2,1) MODELS?
Hi,
I'm a beginner for EViews. Currently I have a file named Canada Xchange Rate (as attached below). I am trying to estimate the GARCH (1,1), (2,2), (1,2) and (2,1) models in one script file. My script file is as follows:
'change path to program path
%path = @runpath
cd %path
' set sample
smpl @all
scalar p=1
scalar q=1
series tt = dlog(value)
freeze tt
arch tt c ar(1)
eq1.makegarch garch1
smpl @all
scalar p=2
scalar q=2
series bt = dlog(value)
freeze bt
arch(2,2) bt c ar(2)
eq1.makegarch garch2
smpl @all
scalar p=1
scalar q=2
series ht = dlog(value)
freeze ht
arch(1,2) ht c ar(2)
eq1.makegarch garch3
smpl @all
scalar p=2
scalar q=1
series kt = dlog(value)
freeze kt
arch(2,1) kt c ar(1)
eq1.makegarch garch4
I would be glad if you could guide me on this. Thank you for your time.
Regards,
Hong
Attachments
simlgl
Posts: 6
Joined: Sat Aug 10, 2013 2:56 am
Re: HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?
I am trying to estimate a BEKK Model where I can analyse volatility spillovers between 4 commodities and 3 stocks, making it a 7x7 matrix. So far, I have got to this point:
smpl @all
series y1 = agriculture
series y2 = crudeoil
series y3 = energy
series y4 = preciousmetal
series y5 = japan
series y6 = uk
series y7 = usa
equation eq1.arch y1 c
equation eq2.arch y2 c
equation eq3.arch y3 c
equation eq4.arch y4 c
equation eq5.arch y5 c
equation eq6.arch y6 c
equation eq7.arch y7 c
eq1.makegarch garch1
eq2.makegarch garch2
eq3.makegarch garch3
eq4.makegarch garch4
eq5.makegarch garch5
eq6.makegarch garch6
eq7.makegarch garch7
coef(7) lambda
lambda(1) = eq1.c(1)
lambda(2) = eq2.c(1)
lambda(3) = eq3.c(1)
lambda(4) = eq4.c(1)
lambda(5) = eq5.c(1)
lambda(6) = eq6.c(1)
lambda(7) = eq7.c(1)
coef(7) mu
mu(1) = eq1.c(2)
mu(2) = eq2.c(2)
mu(3) = eq3.c(2)
mu(4) = eq4.c(2)
mu(5) = eq5.c(2)
mu(6) = eq6.c(2)
mu(7) = eq7.c(2)
coef(3) omega
omega(1)=(eq1.c(3))
omega(1)=(eq1.c(3))
omega(1)=(eq1.c(3))
omega(1)=(eq1.c(3))
omega(1)=(eq1.c(3))
omega(1)=(eq1.c(3))
omega(1)=(eq1.c(3))
However I am not sure about omega and how to declare these coefficients, I understand it should be a 7x7 lower triangular matrix? I have already looked through all of these related posts on here and Im stuck at this point. Is there any help you can give? Ive attached the workfile for viewing
Thanks,
SIMLGL
Attachments
newdataupdated.wf1
garch program.prg
Did you use forum search?
Posts: 1518
Joined: Thu Nov 20, 2008 12:04 pm
Re: HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?
This is just the initialization of coefficients to be used later in the analysis. Omegas are used to construct the constants in the conditional variance equations. I can assure you that you can find all the help an guidance you need in the previous posts of this thread.
simlgl
Posts: 6
Joined: Sat Aug 10, 2013 2:56 am
Re: HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?
trubador wrote:This is just the initialization of coefficients to be used later in the analysis. Omegas are used to construct the constants in the conditional variance equations. I can assure you that you can find all the help an guidance you need in the previous posts of this thread.
Thanks for the reply.It is much appreciated I've gone through all of the posts here but I just need some confirmation.
Am I right in saying that because my omega is a lower traingular 7x7 matrix, there should be 28 omega commands to enter? For example, would this be right to enter?
omega(1)=(eq1.c(3))^.5 (Can you explain why many programs have "^.5?")
omega(2)=0?.................(What is the reason for most programs having omega 2 as 0?
omega(3)=(eq2.c(3))
omega(4)=(eq3.c(3))
omega(5)=(eq4.c(3))
omega(6)=(eq5.c(3))
omega(7)=(eq6.c(3)).............?
And for my alpha and beta coefficients, which are diagonal matrices, there will also will 28 each to satisfy this equation? Thanks again for your help
Regards,
simlgl
Stat_One
Posts: 3
Joined: Sun Oct 13, 2013 10:00 pm
Re: HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?
Hi, do you have the code for the GARCH-M MODEL with 4 times series?? thank.
misscats
Posts: 29
Joined: Wed Mar 19, 2014 8:37 am
Re: HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?
I have modified this set of codes. I am learning the garch-m modelling. If anything sounds stupid, please bear with me.
I have two questions hope you can help me to confirm them:
1. May I ask whether this model is the "constant conditional correlation (ccc)" multivariate garch model?
2. It seems the output does not show the correlation of variances, can I write the below equation to get the correlation of variances?
Code: Select all
`series corr12=cov_y1y2/(var_y1^.5 * var_y2^.5)`
Did you use forum search?
Posts: 1518
Joined: Thu Nov 20, 2008 12:04 pm
Re: HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?
1) No, it is not a CCC model.
2) Yes, that is the formula of correlation.
misscats
Posts: 29
Joined: Wed Mar 19, 2014 8:37 am
Re: HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?
Thanks for your reply. If it is not a ccc model. Which model is it, bekk?
trubador wrote:1) No, it is not a CCC model.
Did you use forum search?
Posts: 1518
Joined: Thu Nov 20, 2008 12:04 pm
Re: HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?
As it is written in the very beginning of the code: "restricted (diagonal) version of tri-variate BEKK".
misscats
Posts: 29
Joined: Wed Mar 19, 2014 8:37 am
Re: HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?
My data is in irregular sample period. I read so many discussions here but no matter how I tried I still got errors:
=================================
Missing values in @LOGL series at current coefficients at observation 12/03/1990 in "DO_ BVGARCH.ML(SHOWOPTS, M=100, C=1E-5)".
LogL estimates are not valid in "SHOW BVGARCH.OUTPUT".
VARCOV is not defined in "SHOW VARCOV".
LogL estimates are not valid in "SCALAR LR = -2*( EQ1.@LOGL + EQ2.@LOGL - BVGARCH.@LOGL )".
LR is not defined in "SCALAR LR_PVAL = 1 - @CCHISQ(LR,1)".
=================================
I attach my workfile and the code here.
(a) which one(s) goes wrong?
(b) With my codes, var_y1, var_y2 and covariance series appear all the same. Is it normal? Are these initial values? So, the output is not successfully generated yet?
(c) As my two equations are with different independent variables. I worry about my covariance equation, may you help me check whether I get it right.
(d) My key result is the correlation of variances. As you have said it is the right equation, is it in the right place of the codes?
Code: Select all
`'get starting values from univariate GARCH'equation eq1.arch(m=100,c=1e-5) y1 c'equation eq2.arch(m=100,c=1e-5) y2 cload 15daysgap.wf1series y1=bm19series y2=fxsample ss'get starting values from univariate GARCHgroup indepvars1 ftallsh fx(-1) ir smb hml mom dummy1 group indepvars2 fx(-1)equation eq1.ARCH(THRSH=1,GED,ARCHM=VAR,S=0,BACKCAST=0.7,DERIV=AA, m=100, c=1e-5) y1 C INDEPVARS1 @ DUMMY1equation eq2.ARCH(THRSH=1,GED,ARCHM=VAR,S=0,BACKCAST=0.7,DERIV=AA, m=100, c=1e-5) y2 C INDEPVARS2 'save the conditional varianceseq1.makegarch garch1eq2.makegarch garch2'Residuals and mueq1.makeresid(s) res1eq2.makeresid(s) res2'declare coef vectors to use in GARCH model ' y = mu + res -> y = mu + H*lambda + res ' res ~ N(0,H) ' ' H = omega*omega' + beta H(-1) beta' + alpha res(-1) res(-1)' alpha' + lev res(-1;<0) + duminvar dummy1 coef(2) lambda lambda(1) = eq1.c(1) lambda(2) = eq2.c(1) y1(1) =na y2(1) =na coef(2) mu mu(1)=@mean(y1-res1-lambda(1)*garch1) mu(2)=@mean(y2-res2-lambda(2)*garch2) coef(3) omega omega(1)=@sqrt(@abs(eq1.c(10))) omega(2)=0 omega(3)=@sqrt(@abs(eq2.c(4))) coef(2) alpha alpha(1) = @sqrt(@abs(eq1.c(11))) alpha(2) = @sqrt(@abs(eq2.c(5))) coef(2) lev lev(1) =@sqrt(@abs(eq1.c(12))) lev(2) =@sqrt(@abs(eq1.c(6))) coef(3) beta beta(1)=@sqrt(@abs(eq1.c(13))) beta(2)=@sqrt(@abs(eq2.c(7))) beta(3)=(beta(1)*beta(2))^.5 coef(1)duminvar duminvar(1)=@sqrt(@abs(eq1.c(14))) ' constant adjustment for log likelihood !mlog2pi = 2*log(2*@acos(-1)) ' use sample var-cov as starting value of variance-covariance matrix ' res1 =y1-mu(1)-lambda(1)*garch1 series cov_y1y2 = @cov(y1-mu(1)-lambda(1)*garch1, y2-mu(2)-lambda(2)*garch2) series var_y1 = @var(y1-lambda(1)*garch1) series var_y2 = @var(y2-lambda(2)*garch2) series sqres1 = (y1-mu(1)-lambda(1)*garch1)^2 series sqres2 = (y2-mu(2)-lambda(2)*garch2)^2 series res1res2 = (y1-mu(1)-lambda(1)*garch1)*(y2-mu(2)-lambda(2)*garch2) series sqresneg1 = (res1<0)^2 series sqresneg2 = (res2<0)^2 series res1res2neg=(res1<0)*(res2<0) ' LOG LIKELIHOOD ' set up the likelihood ' 1) open a new blank likelihood object (L.O.) name bvgarch ' 2) specify the log likelihood model by append ' ........................................................... logl bvgarch ' squared errors and cross errors bvgarch.append @logl logl bvgarch.append sqres1 =( (y1-mu(1)-lambda(1)*garch1)^2) bvgarch.append sqres2 = ((y2-mu(2)-lambda(2)*garch2)^2) bvgarch.append res1res2 = ((y1-mu(1)-lambda(1)*garch1)*(y2-mu(2)-lambda(2)*garch2)) bvgarch.append sqresneg1 = (res1<0)^2 bvgarch.append sqresneg2 = (res2<0)^2 bvgarch.append res1res2neg=(res1<0)*(res2<0) ' calculate the variance and covariance series ' H = omega*omega' + beta H(-1) beta' + alpha res(-1) res(-1)' alpha' + lev res(-1;<0) + duminvar dummy1 bvgarch.append var_y1 = @nan(omega(1)^2 + (beta(1)^2)*var_y1(-1) + (alpha(1)^2)*sqres1(-1) + (lev(1)^2)*sqres1(-1)*sqresneg1(-1)+(duminvar(1)^2)*dummy1,1) bvgarch.append var_y2 = @nan(omega(3)^2 +( beta(2)^2)*var_y2(-1) + (alpha(2)^2)*sqres2(-1) + (lev(2)^2)*sqres1(-1)*sqresneg2(-1),1) bvgarch.append cov_y1y2= @nan(omega(2)+beta(3)*cov_y1y2(-1) + alpha(2)*alpha(1)*res1res2(-1) + lev(2)*lev(1)*sqres1(-1)*res1res2neg(-1) +(duminvar(1)^2)*dummy1,1) ' bvgarch.append cov_y1y2 = omega(1)*omega(2) + beta(2)*beta(1)*cov_y1y2(-1) + alpha(2)*alpha(1)*res1res2(-1) ' determinant of the variance-covariance matrix bvgarch.append deth = var_y1*var_y2 - cov_y1y2^2 ' inverse elements of the variance-covariance matrix bvgarch.append invh1 = var_y2/deth bvgarch.append invh3 = var_y1/deth bvgarch.append invh2 = -cov_y1y2/deth ' log-likelihood series bvgarch.append logl =-0.5*(!mlog2pi + (invh1*sqres1+2*invh2*res1res2+invh3*sqres2) + log(deth)) ' estimate the model smpl ss bvgarch.ml(showopts, m=100, c=1e-5)series res1 = sqres1^.5series res2 = sqres2^.5series stres1 = res1 /(var_y1 ^ .5)series stres2 = res2 /(var_y2 ^ .5)series sqres1st = stres1^2series sqres2st = stres2^2series stres1res2 = res1*res2 /(var_y1*var_y2)^.5series corr12=cov_y1y2/(var_y1^.5 * var_y2^.5)'graph resids1.line stres1 y1'show resids1'graph resids2.line stres2 y2'show resids2 ' change below to display different output show bvgarch.output 'graph varcov.line var_y1 var_y2 cov_y1y2 show varcov ' LR statistic for univariate versus bivariate model scalar lr = -2*( eq1.@logl + eq2.@logl - bvgarch.@logl ) scalar lr_pval = 1 - @cchisq(lr,1)`
Attachments
15daysgap.wf1
Did you use forum search?
Posts: 1518
Joined: Thu Nov 20, 2008 12:04 pm
Re: HOW TO ESTIMATE A MULTIVARIATE GARCH-M MODEL?
misscats wrote:My data is in irregular sample period. I read so many discussions here but no matter how I tried I still got errors:
I really do not have anything new or different to say other than my previous posts under similar threads. For example, I instantly noticed that:
1) You do not define the sample object "ss" anywhere in the code or workfile,
2) Dependent variable y1 have missing values until 10/31/2005.
Unless you successfully estimate the model, you'll keep getting those error messages... | 5,048 | 14,838 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3 | 3 | CC-MAIN-2020-40 | latest | en | 0.781665 |
https://www.slideshare.net/ankitmahapatra22/ray-optics-formulaes | 1,487,548,955,000,000,000 | text/html | crawl-data/CC-MAIN-2017-09/segments/1487501170286.6/warc/CC-MAIN-20170219104610-00400-ip-10-171-10-108.ec2.internal.warc.gz | 915,746,449 | 37,298 | Upcoming SlideShare
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# Ray Optics Formulaes
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A collection of important ray optics formulas.
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### Ray Optics Formulaes
1. 1. Important Ray Optics Formulas
2. 2. Mirror Formula
3. 3. Relation between Refractive indices According to Snell's law By Snell’s law
4. 4. Refractive index
5. 5. Real depth and Apparent depth
6. 6. Total Internal Reflection and Critical angle Total internal reflection occurs when light is passing through a medium (call it 1) like glass or plastic with an index of refraction n1. Outside this material is a medium like air (call it 2) with an index of refraction n2. For certain angles of incidence for light striking the interface and going from medium 1 to medium 2, light will not pass through the interface, but will be totally reflected inside medium 2. This occurs primarily when the light strikes a glancing blow on the interface. For a thin material of medium 2, like a fiber, these angles will always be small, and the light will stay inside the fiber. This process, called total internal reflection.
7. 7. Necessary conditions for Total Internal Reflection a)Light must travel from denser to rarer medium b)The angle of incidence (in denser medium) must be greater than the critical angle where
8. 8. Refraction at Spherical Surfaces 1. When light goes from rarer to denser medium through a spherical surface Having radius of curvature R. 2.When light goes from denser to rarer through a spherical surface
9. 9. The Lens Formula
10. 10. Linear Magnification For mirrors : For lenses :
11. 11. (Take care that f is in meter) * For thin lenses in contact :
12. 12. * Thin lenses placed at a distance d: (For two lenses)
13. 13. Refraction through a prism
14. 14. When the angle of incidence is such that the refracted ray inside the prism is parallel to the base of the prism , the prism is said to be in a position of minimum deviation. Under this condition From Snell’s law (where is angle of minimum deviation)
15. 15. Dispersion of light Splitting up of white light into its constituent colours on passing through a medium is called dispersion of light and the medium of dispersion is called dispersive medium. # Dispersion of light is owing to the fact that velocity of light of different wavelengths is different in a material medium . # Angle of dispersion depends upon angle of prism and material of prism. # According to Cauchy’s Formula :
16. 16. Angular Dispersion For white light it is equal to the difference in the angle of deviation fro two extreme colours i.e., violet and red. *Angular separation between violet and red wavelengths/colours produced by a prism is called angular dispersion. *Mathematically
17. 17. Dispersive Power The ratio of angular dispersion to the angle of deviation for the mean wavelength (yellow colour) is called dispersive power of the material of the prism. Thus dispersive power , ω can be written as : * Dispersive Power is independent of angle of prism but dependent upon material of prism.
18. 18. Optical Instruments
19. 19. Simple Microscope * Magnifying Power when image is formed at least distance of distinct vision . * Magnifying power when final image is formed at infinity
20. 20. Compound Microscope (*Two conves lenses are used. *Aperture and focal length of objective lens are smaller as compared to those of eye piece) #When final image is formed at infinity #When final image is formed at least distance of distinct vision
21. 21. Astronomical Telescope *Objective is a convex lens of large aperture and large focal length whereas eye piece is also a convex lens of smaller focal length *When final image is formed at distance of distinct vision , the magnifying power is given by *When final image is formed at infinity (telescope is said to be at normal adjustment) , the magnifying power is given as
22. 22. Reflecting Type telescope It was designed by Newton. Used for observing distant stars. *In normal adjustment , magnifying power of a reflecting type telescope is :
23. 23. Resolving Power •It is the reciprocal of limit of resolution. •It is an ability of an instrument to resolve the images of two points lying close to each other . •Resolving power of a microscope is : Θ is the half angle subtended on to the objective lens by the cone of light from the point object under observation . D is the minimum distance between the two point object under observation. * d is the minimum distance between the two point objects for which they can be seen as separate objects through a microscope *Resolving power of a telescope : *Where D is aperture of objective of the telescope or diameter of the objective lens. *dΘ is the angle subtended at the objective by the two point objects
24. 24. Thank You for Viewing It. | 1,175 | 5,081 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.296875 | 3 | CC-MAIN-2017-09 | latest | en | 0.781783 |
https://www.morevisibility.com/blogs/analytics/the-difference-between-bounce-rate-and-exit-percentage.html/amp | 1,529,913,086,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267867579.80/warc/CC-MAIN-20180625072642-20180625092642-00135.warc.gz | 872,694,227 | 6,097 | # The difference between Bounce Rate and Exit Percentage
Greetings, and welcome to the new MoreVisibility Analytics and Site Intelligence Blog! My name is Joe Teixeira, and I’m the Manager of Web Intelligence here at MoreVisibility. I’ll be doing most of the posting here, but from time to time, some of my co-workers and colleagues will join in on the fun.
I was thinking of what my first blog post would be about, and I’ve decided to talk about one of the most common items that is brought up in Web Analytics discussions, especially for newcomers to Web Analytics. Most analytics packages, like Google Analytics, show a metric named “Bounce Rate”, and also show a metric named “Exit %”, or “Exit Percentage”. At first glance, these metrics may look very similar, and you may even interpret them to mean the same thing. However, they are two COMPLETELY separate metrics, calculated two entirely different ways.
First, lets define a “Bounce”. A “Bounce” is a single-page visit to your website. For example, John lands on your homepage, www.xyz.com, and leaves your site without visiting any other pages on your website – that’s a “Bounce”. The “Bounce Rate” is calculated by taking the total number of Bounces (to your website or a set of pages, depending on what you’re looking at), and dividing it by the total number of Visits (to your website or a set of pages, depending on what you’re looking at).
The Exit Percentage is calculated by taking the total number of Exits, and dividing them by the total number of Pageviews (Not Visits – Pageviews). The Exit Percentage doesn’t care whether or not any of the Pageviews were from visitors who viewed 1 page, or viewed 1,000 pages – it simply does the math, and prints it in your Web Analytics interface.
Usually after explaining this difference, the follow-up questions that I usually get are “So, which one do I look at? / Which one do I use?”
I have a pretty simple rule: “Never make any analysis based off of one metric or one statistic”. So, you should never think of “looking” or “using” one individual metric to make any kind of decisions – you should always look at the complete picture of your website’s data, and then go from there. However, every rule has an exception, and this one is no different. If there was any metric in Web Analytics that you could make a very strong argument for using by itself, without the support of any other metrics, it would be the Bounce Rate. Think about what the Bounce Rate is calculating – it’s calculating the percentage of visits to your website who viewed one page on your website, and then left. If the visitors to your website were engaged and reacted positively to your website when they first landed on it, wouldn’t you think they would at least visit another page on your site, instead of leaving it entirely? Especially if you are looking for people to interact and visit the other pages on your site?
With Exit Percentage, all you can say is “This Percentage of Exits happened from this page / this set of pages”, without separating visits that Bounced from visits that did not Bounce. It’s impossible to draw any conclusions or formulate any hypotheses from this, as you can from the Bounce Rate metric. Also, keep in mind that, at some point in time, a visitor to your website ultimately has to leave your website (unless they are some sort of android that can stay awake and on a website infinitely).
So, I would recommend for you to pay close attention to your Bounce Rate – especially if you have a website featuring multiple pages (not counting blogs or single informational pages). Of course, the lower the Bounce Rate, the better, and the more engaged visitors are with your website. I can’t give you any kind of solid figure or benchmark on what your Bounce Rate should look like, but chances are that if 2 out of every 3 visits to your website are Bouncing, you may have a big problem that requires your immediate attention. If 1 out of three (or less) are Bouncing, chances are probably pretty good that you’re doing something right. | 871 | 4,060 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.84375 | 3 | CC-MAIN-2018-26 | longest | en | 0.946793 |
https://number.academy/18802 | 1,656,174,392,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103036077.8/warc/CC-MAIN-20220625160220-20220625190220-00283.warc.gz | 466,566,117 | 12,218 | # Number 18802
Number 18,802 spell 🔊, write in words: eighteen thousand, eight hundred and two . Ordinal number 18802th is said 🔊 and write: eighteen thousand, eight hundred and second. The meaning of number 18802 in Maths: Is Prime? Factorization and prime factors tree. The square root and cube root of 18802. What is 18802 in computer science, numerology, codes and images, writing and naming in other languages. Other interesting facts related to 18802.
## What is 18,802 in other units
The decimal (Arabic) number 18802 converted to a Roman number is (X)(V)MMMDCCCII. Roman and decimal number conversions.
#### Weight conversion
18802 kilograms (kg) = 41450.9 pounds (lbs)
18802 pounds (lbs) = 8528.5 kilograms (kg)
#### Length conversion
18802 kilometers (km) equals to 11684 miles (mi).
18802 miles (mi) equals to 30259 kilometers (km).
18802 meters (m) equals to 61686 feet (ft).
18802 feet (ft) equals 5731 meters (m).
18802 centimeters (cm) equals to 7402.4 inches (in).
18802 inches (in) equals to 47757.1 centimeters (cm).
#### Temperature conversion
18802° Fahrenheit (°F) equals to 10427.8° Celsius (°C)
18802° Celsius (°C) equals to 33875.6° Fahrenheit (°F)
#### Time conversion
(hours, minutes, seconds, days, weeks)
18802 seconds equals to 5 hours, 13 minutes, 22 seconds
18802 minutes equals to 1 week, 6 days, 1 hour, 22 minutes
### Codes and images of the number 18802
Number 18802 morse code: .---- ---.. ---.. ----- ..---
Sign language for number 18802:
Number 18802 in braille:
Images of the number
Image (1) of the numberImage (2) of the number
More images, other sizes, codes and colors ...
## Mathematics of no. 18802
### Multiplications
#### Multiplication table of 18802
18802 multiplied by two equals 37604 (18802 x 2 = 37604).
18802 multiplied by three equals 56406 (18802 x 3 = 56406).
18802 multiplied by four equals 75208 (18802 x 4 = 75208).
18802 multiplied by five equals 94010 (18802 x 5 = 94010).
18802 multiplied by six equals 112812 (18802 x 6 = 112812).
18802 multiplied by seven equals 131614 (18802 x 7 = 131614).
18802 multiplied by eight equals 150416 (18802 x 8 = 150416).
18802 multiplied by nine equals 169218 (18802 x 9 = 169218).
show multiplications by 6, 7, 8, 9 ...
### Fractions: decimal fraction and common fraction
#### Fraction table of 18802
Half of 18802 is 9401 (18802 / 2 = 9401).
One third of 18802 is 6267,3333 (18802 / 3 = 6267,3333 = 6267 1/3).
One quarter of 18802 is 4700,5 (18802 / 4 = 4700,5 = 4700 1/2).
One fifth of 18802 is 3760,4 (18802 / 5 = 3760,4 = 3760 2/5).
One sixth of 18802 is 3133,6667 (18802 / 6 = 3133,6667 = 3133 2/3).
One seventh of 18802 is 2686 (18802 / 7 = 2686).
One eighth of 18802 is 2350,25 (18802 / 8 = 2350,25 = 2350 1/4).
One ninth of 18802 is 2089,1111 (18802 / 9 = 2089,1111 = 2089 1/9).
show fractions by 6, 7, 8, 9 ...
### Calculator
18802
#### Is Prime?
The number 18802 is not a prime number. The closest prime numbers are 18797, 18803.
#### Factorization and factors (dividers)
The prime factors of 18802 are 2 * 7 * 17 * 79
The factors of 18802 are
1 , 2 , 7 , 14 , 17 , 34 , 79 , 119 , 158 , 238 , 553 , 1106 , 1343 , 2686 , 9401 , 18802
Total factors 16.
Sum of factors 34560 (15758).
#### Powers
The second power of 188022 is 353.515.204.
The third power of 188023 is 6.646.792.865.608.
#### Roots
The square root √18802 is 137,120385.
The cube root of 318802 is 26,591001.
#### Logarithms
The natural logarithm of No. ln 18802 = loge 18802 = 9,841719.
The logarithm to base 10 of No. log10 18802 = 4,274204.
The Napierian logarithm of No. log1/e 18802 = -9,841719.
### Trigonometric functions
The cosine of 18802 is -0,908117.
The sine of 18802 is 0,418717.
The tangent of 18802 is -0,461082.
### Properties of the number 18802
Is a Friedman number: No
Is a Fibonacci number: No
Is a Bell number: No
Is a palindromic number: No
Is a pentagonal number: No
Is a perfect number: No
## Number 18802 in Computer Science
Code typeCode value
18802 Number of bytes18.4KB
Unix timeUnix time 18802 is equal to Thursday Jan. 1, 1970, 5:13:22 a.m. GMT
IPv4, IPv6Number 18802 internet address in dotted format v4 0.0.73.114, v6 ::4972
18802 Decimal = 100100101110010 Binary
18802 Decimal = 221210101 Ternary
18802 Decimal = 44562 Octal
18802 Decimal = 4972 Hexadecimal (0x4972 hex)
18802 BASE64MTg4MDI=
18802 MD5ba29c0a9d05316b187201c304b20120d
18802 SHA1f075502dc4ff016573120792eae1b15520308a62
18802 SHA256ea3089bbba0c99d29c5813742e81ddd1d223c776164a2353ea6b5b7094724d69
18802 SHA384f15c70233946c5980ddd8bb9e62a3b1418d88832cb40f14f60aba10d9f2e9934960a30e857159ba49c48d9047871cd07
More SHA codes related to the number 18802 ...
If you know something interesting about the 18802 number that you did not find on this page, do not hesitate to write us here.
## Numerology 18802
### Character frequency in number 18802
Character (importance) frequency for numerology.
Character: Frequency: 1 1 8 2 0 1 2 1
### Classical numerology
According to classical numerology, to know what each number means, you have to reduce it to a single figure, with the number 18802, the numbers 1+8+8+0+2 = 1+9 = 1+0 = 1 are added and the meaning of the number 1 is sought.
## Interesting facts about the number 18802
### Asteroids
• (18802) 1999 JR76 is asteroid number 18802. It was discovered by LINEAR, Lincoln Near-Earth Asteroid Research from Lincoln Laboratory, Socorro on 5/10/1999.
### Distances between cities
• There is a 11,684 miles (18,802 km) direct distance between Guayaquil (Ecuador) and Ho Chi Minh City (Viet Nam).
• There is a 11,684 miles (18,802 km) direct distance between Guayaquil (Ecuador) and Jakarta (Indonesia).
• There is a 11,684 miles (18,802 km) direct distance between Lima (Peru) and Singapore (Singapore).
• There is a 11,684 miles (18,802 km) direct distance between Santiago (Chile) and Yunfu (China).
• More distances between cities ...
## Number 18,802 in other languages
How to say or write the number eighteen thousand, eight hundred and two in Spanish, German, French and other languages. The character used as the thousands separator.
Spanish: 🔊 (número 18.802) dieciocho mil ochocientos dos German: 🔊 (Anzahl 18.802) achtzehntausendachthundertzwei French: 🔊 (nombre 18 802) dix-huit mille huit cent deux Portuguese: 🔊 (número 18 802) dezoito mil, oitocentos e dois Chinese: 🔊 (数 18 802) 一万八千八百零二 Arabian: 🔊 (عدد 18,802) ثمانية عشر ألفاً و ثمانمائة و اثنان Czech: 🔊 (číslo 18 802) osmnáct tisíc osmset dva Korean: 🔊 (번호 18,802) 만 팔천팔백이 Danish: 🔊 (nummer 18 802) attentusinde og ottehundrede og to Dutch: 🔊 (nummer 18 802) achttienduizendachthonderdtwee Japanese: 🔊 (数 18,802) 一万八千八百二 Indonesian: 🔊 (jumlah 18.802) delapan belas ribu delapan ratus dua Italian: 🔊 (numero 18 802) diciottomilaottocentodue Norwegian: 🔊 (nummer 18 802) atten tusen, åtte hundre og to Polish: 🔊 (liczba 18 802) osiemnaście tysięcy osiemset dwa Russian: 🔊 (номер 18 802) восемнадцать тысяч восемьсот два Turkish: 🔊 (numara 18,802) onsekizbinsekizyüziki Thai: 🔊 (จำนวน 18 802) หนึ่งหมื่นแปดพันแปดร้อยสอง Ukrainian: 🔊 (номер 18 802) вiсiмнадцять тисяч вiсiмсот двi Vietnamese: 🔊 (con số 18.802) mười tám nghìn tám trăm lẻ hai Other languages ...
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## Comment
If you know something interesting about the number 18802 or any natural number (positive integer) please write us here or on facebook. | 2,519 | 7,375 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.21875 | 3 | CC-MAIN-2022-27 | latest | en | 0.680836 |
https://thisisbeep.com/how-do-you-find-the-pi-of-an-amino-acid/ | 1,653,055,357,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662532032.9/warc/CC-MAIN-20220520124557-20220520154557-00568.warc.gz | 667,757,178 | 12,274 | # How do you find the pI of an amino acid?
## How do you find the pI of an amino acid?
61 second suggested clip7:5712:45How To Calculate The Isoelectric Point of Amino Acids and ZwitterionsYouTubeStart of suggested clipEnd of suggested clipSo to calculate the isoelectric. Point of this order ion we need to average. These two PKA values.MoreSo to calculate the isoelectric. Point of this order ion we need to average. These two PKA values. So it’s going to be eight point nine five plus ten point five divided by two.
## How do you calculate the net charge of a peptide?
57 second suggested clip0:0822:53How to Calculate Peptide Charge and Isoelectric Point MCAT TrickYouTubeStart of suggested clipEnd of suggested clipWhen you’re looking at a peptide you have to take all ionizable. Groups into account but with parentMoreWhen you’re looking at a peptide you have to take all ionizable. Groups into account but with parent and sidechain add up all the charges. And that will give you the net charge.
## How do you find the length of a polypeptide chain?
The length of a polypeptide with 20 residues can be determined by looking at the angles and bond lengths of a segment of amino acids. Note: The bond lengths are highlighted in blue, the total angle is in magenta, and half of the angle is in red. (a) Calculate the length of an alpha helical section with 20 residues.
## How do you calculate pI?
The formula for the value of pi is the ratio of the circumference of a circle to its diameter. In the ratio form, it is represented as π = Circumference/Diameter.
## What is pI in amino acids?
The isoelectric point (pI) is the pH value at which the molecule carries no electrical charge. For an amino acid, the isoelectric point is the average of pKa values for the amine and the carboxyl group.
## How is MCAT pI calculated?
53 second suggested clip2:3218:34Isoelectric Point of Amino Acids with MCAT Shortcut – YouTubeYouTube
## What are the charged amino acids?
Among the 20 common amino acids, five have a side chain which can be charged. At pH=7, two are negative charged: aspartic acid (Asp, D) and glutamic acid (Glu, E) (acidic side chains), and three are positive charged: lysine (Lys, K), arginine (Arg, R) and histidine (His, H) (basic side chains).
## How do you find the amount of amino acids in a polypeptide chain?
53 second suggested clip2:506:48How to find a number of Amino acids in protein chain? – YouTubeYouTube
## How do you calculate the length of an amino acid?
1. Relative amino acid = Total no of individual aa/total no. of aa x100.
2. average amino acid = relative aa/total no. of protein.
3. total. no of specific aa/total no. of protein sequences.
4. avg.
The pI is the pH at which the average charge of all of the amino acid species in solution is zero. Select an amino acid, then drag the pH arrow around to see how the percentages of amino acid species and the total net charge change with pH. Find the point where the average charge is 0.
## What is the amino acid calculator?
The Amino Acid Calculatoris a handy tool for analyzing individual sequences – it can translate genetic code to amino acid sequence, check for errors in nucleotide and amino acid sequences, determine their physical parameters, and design primers. Fields Open Amino Acid Calculator Amino Acid CalculatorMenu
## What are the PKA and pi values of amino acids?
pKa and pI values of amino acids Amino acid 3-letter code 1-letter code pKa Cα -COOH pKa Cα -NH 3 + pKa side chain Isoelectric point (pI) Alanine Ala A 2.34 9.69 – 6.02 Arginine Arg R 2.17 9.04 12.48 10.76 Asparagine Asn N 2.02 8.80 – 5.41 Aspartic acid Asp D 2.09 9.82 3.86 2.98
## What is the P I of an amino acid?
For this we should refer to the titration curve of the amino acid. From the curve we can infer that the p I is simply the average of the two p K a values of the carboxylic acid and the amino group. From the curve we can infer that the p I is simply the average of the two p K a values of the two amino groups. | 1,018 | 4,018 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.15625 | 3 | CC-MAIN-2022-21 | latest | en | 0.872894 |
http://mathhelpforum.com/trigonometry/58827-sum-difference.html | 1,527,069,135,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794865468.19/warc/CC-MAIN-20180523082914-20180523102914-00156.warc.gz | 186,640,696 | 9,719 | 1. ## Sum and Difference
$\displaystyle \tan(A + B)={-7/6}, \tan(B)={5/3}$
Find tan(A)
2. use the sum identity ...
$\displaystyle \tan(a+b) = \frac{\tan{a} + \tan{b}}{1 - \tan{a}\tan{b}}$
sub in what you know, solve for $\displaystyle \tan{a}$
3. and how would i solve for tan(a), not sure where to start.
4. $\displaystyle \tan(a+b) = \frac{\tan{a} + \tan{b}}{1 - \tan{a}\tan{b}}$
$\displaystyle \tan(a+b) (1 - \tan{a}\tan{b}) = \tan{a} + \tan{b}$
$\displaystyle \tan(a+b) - \tan(a+b) \tan{a} \tan{b} = \tan{a} + \tan{b}$
$\displaystyle \tan(a+b) - \tan{b} = \tan{a} - \tan(a+b) \tan{a} \tan{b}$
$\displaystyle \tan(a+b) - \tan{b} = \tan{a}[1 - \tan(a+b) \tan{b}]$
$\displaystyle \frac{\tan(a+b) - \tan{b}}{1 - \tan(a+b) \tan{b}} = \tan{a}$ | 325 | 753 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.15625 | 4 | CC-MAIN-2018-22 | latest | en | 0.37425 |
https://docs.rs/malachite-base/latest/malachite_base/num/arithmetic/traits/trait.DivRound.html | 1,701,247,964,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100057.69/warc/CC-MAIN-20231129073519-20231129103519-00669.warc.gz | 252,075,337 | 12,111 | # Trait malachite_base::num::arithmetic::traits::DivRound
pub trait DivRound<RHS = Self> {
type Output;
// Required method
fn div_round(self, other: RHS, rm: RoundingMode) -> (Self::Output, Ordering);
}
Expand description
Divides a number by another number and rounds according to a specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.
source
source
## Implementations on Foreign Types§
source§
### impl DivRound for i8
source§
#### fn div_round(self, other: i8, rm: RoundingMode) -> (i8, Ordering)
Divides a value by another value and rounds according to a specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.
Let $q = \frac{x}{y}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:
$$g(x, y, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$$
$$g(x, y, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$$
$$g(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$$
$$g(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$$
$$g(x, y, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd.} \end{cases}$$
$g(x, y, \mathrm{Exact}) = q$, but panics if $q \notin \Z$.
Then
$f(x, y, r) = (g(x, y, r), \operatorname{cmp}(g(x, y, r), q))$.
##### Panics
Panics if other is zero, if self is Self::MIN and other is -1, or if rm is Exact but self is not divisible by other.
See here.
§
source§
### impl DivRound for i16
source§
#### fn div_round(self, other: i16, rm: RoundingMode) -> (i16, Ordering)
Divides a value by another value and rounds according to a specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.
Let $q = \frac{x}{y}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:
$$g(x, y, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$$
$$g(x, y, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$$
$$g(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$$
$$g(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$$
$$g(x, y, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd.} \end{cases}$$
$g(x, y, \mathrm{Exact}) = q$, but panics if $q \notin \Z$.
Then
$f(x, y, r) = (g(x, y, r), \operatorname{cmp}(g(x, y, r), q))$.
##### Panics
Panics if other is zero, if self is Self::MIN and other is -1, or if rm is Exact but self is not divisible by other.
See here.
§
source§
### impl DivRound for i32
source§
#### fn div_round(self, other: i32, rm: RoundingMode) -> (i32, Ordering)
Divides a value by another value and rounds according to a specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.
Let $q = \frac{x}{y}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:
$$g(x, y, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$$
$$g(x, y, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$$
$$g(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$$
$$g(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$$
$$g(x, y, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd.} \end{cases}$$
$g(x, y, \mathrm{Exact}) = q$, but panics if $q \notin \Z$.
Then
$f(x, y, r) = (g(x, y, r), \operatorname{cmp}(g(x, y, r), q))$.
##### Panics
Panics if other is zero, if self is Self::MIN and other is -1, or if rm is Exact but self is not divisible by other.
See here.
§
source§
### impl DivRound for i64
source§
#### fn div_round(self, other: i64, rm: RoundingMode) -> (i64, Ordering)
Divides a value by another value and rounds according to a specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.
Let $q = \frac{x}{y}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:
$$g(x, y, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$$
$$g(x, y, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$$
$$g(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$$
$$g(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$$
$$g(x, y, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd.} \end{cases}$$
$g(x, y, \mathrm{Exact}) = q$, but panics if $q \notin \Z$.
Then
$f(x, y, r) = (g(x, y, r), \operatorname{cmp}(g(x, y, r), q))$.
##### Panics
Panics if other is zero, if self is Self::MIN and other is -1, or if rm is Exact but self is not divisible by other.
See here.
§
source§
### impl DivRound for i128
source§
#### fn div_round(self, other: i128, rm: RoundingMode) -> (i128, Ordering)
Divides a value by another value and rounds according to a specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.
Let $q = \frac{x}{y}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:
$$g(x, y, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$$
$$g(x, y, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$$
$$g(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$$
$$g(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$$
$$g(x, y, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd.} \end{cases}$$
$g(x, y, \mathrm{Exact}) = q$, but panics if $q \notin \Z$.
Then
$f(x, y, r) = (g(x, y, r), \operatorname{cmp}(g(x, y, r), q))$.
##### Panics
Panics if other is zero, if self is Self::MIN and other is -1, or if rm is Exact but self is not divisible by other.
See here.
§
source§
### impl DivRound for isize
source§
#### fn div_round(self, other: isize, rm: RoundingMode) -> (isize, Ordering)
Divides a value by another value and rounds according to a specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.
Let $q = \frac{x}{y}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:
$$g(x, y, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$$
$$g(x, y, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$$
$$g(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$$
$$g(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$$
$$g(x, y, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd.} \end{cases}$$
$g(x, y, \mathrm{Exact}) = q$, but panics if $q \notin \Z$.
Then
$f(x, y, r) = (g(x, y, r), \operatorname{cmp}(g(x, y, r), q))$.
##### Panics
Panics if other is zero, if self is Self::MIN and other is -1, or if rm is Exact but self is not divisible by other.
See here.
§
source§
### impl DivRound for u8
source§
#### fn div_round(self, other: u8, rm: RoundingMode) -> (u8, Ordering)
Divides a value by another value and rounds according to a specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.
Let $q = \frac{x}{y}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:
$$g(x, y, \mathrm{Down}) = g(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$$
$$g(x, y, \mathrm{Up}) = g(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$$
$$g(x, y, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd.} \end{cases}$$
$g(x, y, \mathrm{Exact}) = q$, but panics if $q \notin \N$.
Then
$f(x, y, r) = (g(x, y, r), \operatorname{cmp}(g(x, y, r), q))$.
##### Panics
Panics if other is zero, or if rm is Exact but self is not divisible by other.
See here.
§
source§
### impl DivRound for u16
source§
#### fn div_round(self, other: u16, rm: RoundingMode) -> (u16, Ordering)
Divides a value by another value and rounds according to a specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.
Let $q = \frac{x}{y}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:
$$g(x, y, \mathrm{Down}) = g(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$$
$$g(x, y, \mathrm{Up}) = g(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$$
$$g(x, y, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd.} \end{cases}$$
$g(x, y, \mathrm{Exact}) = q$, but panics if $q \notin \N$.
Then
$f(x, y, r) = (g(x, y, r), \operatorname{cmp}(g(x, y, r), q))$.
##### Panics
Panics if other is zero, or if rm is Exact but self is not divisible by other.
See here.
§
source§
### impl DivRound for u32
source§
#### fn div_round(self, other: u32, rm: RoundingMode) -> (u32, Ordering)
Divides a value by another value and rounds according to a specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.
Let $q = \frac{x}{y}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:
$$g(x, y, \mathrm{Down}) = g(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$$
$$g(x, y, \mathrm{Up}) = g(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$$
$$g(x, y, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd.} \end{cases}$$
$g(x, y, \mathrm{Exact}) = q$, but panics if $q \notin \N$.
Then
$f(x, y, r) = (g(x, y, r), \operatorname{cmp}(g(x, y, r), q))$.
##### Panics
Panics if other is zero, or if rm is Exact but self is not divisible by other.
See here.
§
source§
### impl DivRound for u64
source§
#### fn div_round(self, other: u64, rm: RoundingMode) -> (u64, Ordering)
Divides a value by another value and rounds according to a specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.
Let $q = \frac{x}{y}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:
$$g(x, y, \mathrm{Down}) = g(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$$
$$g(x, y, \mathrm{Up}) = g(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$$
$$g(x, y, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd.} \end{cases}$$
$g(x, y, \mathrm{Exact}) = q$, but panics if $q \notin \N$.
Then
$f(x, y, r) = (g(x, y, r), \operatorname{cmp}(g(x, y, r), q))$.
##### Panics
Panics if other is zero, or if rm is Exact but self is not divisible by other.
See here.
§
source§
### impl DivRound for u128
source§
#### fn div_round(self, other: u128, rm: RoundingMode) -> (u128, Ordering)
Divides a value by another value and rounds according to a specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.
Let $q = \frac{x}{y}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:
$$g(x, y, \mathrm{Down}) = g(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$$
$$g(x, y, \mathrm{Up}) = g(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$$
$$g(x, y, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd.} \end{cases}$$
$g(x, y, \mathrm{Exact}) = q$, but panics if $q \notin \N$.
Then
$f(x, y, r) = (g(x, y, r), \operatorname{cmp}(g(x, y, r), q))$.
##### Panics
Panics if other is zero, or if rm is Exact but self is not divisible by other.
See here.
§
source§
### impl DivRound for usize
source§
#### fn div_round(self, other: usize, rm: RoundingMode) -> (usize, Ordering)
Divides a value by another value and rounds according to a specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.
Let $q = \frac{x}{y}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:
$$g(x, y, \mathrm{Down}) = g(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$$
$$g(x, y, \mathrm{Up}) = g(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$$
$$g(x, y, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd.} \end{cases}$$
$g(x, y, \mathrm{Exact}) = q$, but panics if $q \notin \N$.
Then
$f(x, y, r) = (g(x, y, r), \operatorname{cmp}(g(x, y, r), q))$.
##### Panics
Panics if other is zero, or if rm is Exact but self is not divisible by other.
See here.
§ | 5,983 | 16,737 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2023-50 | latest | en | 0.602127 |
https://www.unifolks.com/questions/calculus-home-work-due-monday-16-2013-1-let-fx-3x2-5x-2-evaluate-limx-2-fx-2-371483.html | 1,652,941,893,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662525507.54/warc/CC-MAIN-20220519042059-20220519072059-00729.warc.gz | 1,223,811,356 | 44,859 | # Calculus Home work Due Monday 16, XXXXXXXXXXLet f(x) = 3x2 - 5x + 2. Evaluate limx?-2 f(x). 2. Calculate limx?2 x2-4 x XXXXXXXXXXCalculate limt?1 5t2+6t+1 8t XXXXXXXXXXCalculate limx?3vx XXXXXXXXXX 5....
Calculus Home work Due Monday 16, XXXXXXXXXXLet f(x) = 3x2 - 5x + 2. Evaluate limx?-2 f(x). 2. Calculate limx?2 x2-4 x XXXXXXXXXXCalculate limt?1 5t2+6t+1 8t XXXXXXXXXXCalculate limx?3vx XXXXXXXXXX
5. Let f(x) = 3b v4b+1-1. Find limb?2 f(b) and limb?0 f(b). The first limit is very easy, the second requires some manipulation on your part.
6. (One-sided limits)
Let f(x) =
0 if x = 2 v25 - x2 if 2
Compute the following limits (a) limx?5- f(x), (b)limx?5+ f(x), (c)limx?5 f(x) ,limx?2- f(x), (d)limx?2+ f(x), (e)limx?2 f(x), (f) limx?100 f(x) 7. Calculate limh?0 v16+h-4 h 8.Assume limx?3 g(x) and f(x) = g(x) whenever x =? 3. What is limx?3 f(x)? Explain your answer.
Note that all these problems are from Section 2.3. Pleasee work out as many as you can from this section. I can put too many problems on the homework–I expect you to workout as many problems as you can from the Book.
1
Document Preview:
Calculus Home work Due Monday 16, 201321. Let f(x) = 3x 5x + 2. Evaluate lim f(x).x!22x42. Calculate lim .x!2x225t +6t+13. Calculate lim .t!18t4p324. Calculate lim x 10.x!33bp5. Let f(x) = . Find lim f(b) and lim f(b). The rst limit is very easy,b!2 b!04b+11the second requires some manipulation on your part.6. (One-sided limits)8>0 if x 2<><>:3x if x 5Compute the following limits (a) lim f(x), (b)lim +f(x), (c)lim f(x) ,lim f(x),x!5 x!5 x!5 x!2+(d)lim f(x), (e)lim f(x), (f) lim f(x)x!2 x!2 x!100p16+h47. Calculate limh!0h8.Assume lim g(x) and f(x) = g(x) whenever x =6 3. What is lim f(x)? Explainx!3 x!3your answer.Note that all these problems are from Section 2.3. Pleasee work out as many as you canfrom this section. I can put too many problems on the homework{I expect you to workoutas many problems as you can from the Book.1
## Solution
Robert answered on Dec 31 2021
Sol: (1) 23 5 2f x x x
2
2 2
2
2
lim lim 3 5 2
3 2 5 2 2
12 10 2
lim 24
x x
x
f x x x
f x
Sol: (2)
2
2 2
2
2
2
2 24
lim lim
2 2
lim 2
2 2
4
lim 4
2
x x
x
x
x xx
x x
x
x
x
Sol: (3)
22
1
2
1
5 1 6 1 15 6 1
lim
8 4 8 1 4
5 6 1
8 4
12
4
5 6 1
lim 3
8 4
t
t
t t
t
t t
t
Sol: (4)
223 3
3
3
3
3
23
3
lim 10 3 10
9 10
1
1 3
lim 10
2 2
x
i
x
x
e
i
x
Sol: (5)
3
4 1 1
f x
(a)
2 2
2
3
lim lim
4 1 1
3 2
4 2 1 1
6
8 1 1
6
9...
SOLUTION.PDF | 1,359 | 2,613 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.03125 | 4 | CC-MAIN-2022-21 | latest | en | 0.822142 |
https://www.tutocad.com/faq/you-asked-how-to-use-scale-on-autocad/ | 1,726,180,577,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651498.46/warc/CC-MAIN-20240912210501-20240913000501-00089.warc.gz | 971,449,348 | 22,592 | Faq
You asked: How to use scale on autocad?
How to scale up in AutoCAD – Window select the object(s), type SCALE, and then specify a number larger than 1. Hit Enter. The size of the object(s) will SCALE UP by that scale factor. Refer to Figure 1 to see the differences in scale factors.
Also the question is, what do you mean by 1 100 scale in AutoCAD? A scale is shown as a ratio, for example 1:100. A drawing at a scale of 1:100 means that the object is 100 times smaller than in real life scale 1:1. You could also say, 1 unit in the drawing is equal to 100 units in real life.
Considering this, how do you scale a layout in AutoCAD?
1. Select the layout viewport that you want to modify.
2. Right-click, and then choose Properties.
3. If necessary, click Display Locked and choose No.
4. In the Properties palette, select Standard Scale, and then select a new scale from the list. The scale you choose is applied to the viewport.
Correspondingly, how do you use a 1 100 scale? A scale of 1 to 100 is indicated on a drawing using the code 1:100. This can be interpreted as follows: 1 centimetre (0.01 metre) measured with a ruler on the plan would need to be multiplied by 100 to give the actual size of 1 metre.
In this regard, how do you scale a drawing? To scale a drawing by hand, start by measuring the width and height of the object you’ll be scaling. Next, choose a ratio to resize your drawing, such as 2 to 1 to double the image in size. Then, multiply your measurements by the first number in your ratio to increase the size.
INTERESTING: You asked: Autocad drawing to excel converter?
Contents
What is the meaning of 1 100 scale?
Ratio scales If the scale of the plan is 1 : 100, this means the real measurements are 100 times longer than they are on the plan. So 1 cm on the plan represents a real length of 100 cm (1 metre)
How do you calculate scale size?
The scale factor is commonly expressed as 1:n or 1/n, where n is the factor. For example, if the scale factor is 1:8 and the real measurement is 32, divide 32 ÷ 8 = 4 to convert. To convert a scaled measurement up to the actual measurement, simply multiply the smaller measurement by the scale factor.
What does the scale 1 50 mean?
1:50 is a ratio. it means you’re scaling 1 unit to 50 units. that could be inches (1″=50″) or miles (1 mile=50 miles) or anything else, but it’s a direct scale. that works better in metric, because their units scale in multiples of 10.
What does the scale 1 1000 mean?
Therefore scale 1:1000 means that one centimeter (one hundredth of a meter, i.e. 0.01m) in the drawing corresponds to 0.01m x 1000 = 10 meters. Similarly, a distance of five meters is drawn as 5m / 1000 = 0.005m = 5 millimeters.
How do you scale an image?
Step 1: Right-click on the image and select Open. If Preview is not your default image viewer, select Open With followed by Preview instead. Step 2: Select Tools on the menu bar. Step 3: Select Adjust Size on the drop-down menu.
INTERESTING: Autocad change background color?
How does scale work in drawings?
The scale is shown as the length in the drawing, then a colon (“:”), then the matching length on the real thing. Example: this drawing has a scale of “1:10”, so anything drawn with the size of “1” would have a size of “10” in the real world, so a measurement of 150mm on the drawing would be 1500mm on the real horse.
How do you reference with a scale?
1. Select the Scale command.
2. Select the desired object.
3. Specify the current distance.
4. Specify the new intended size.
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Please disable your ad blocker to be able to view the page content. For an independent site with free content, it's literally a matter of life and death to have ads. Thank you for your understanding! Thanks | 962 | 3,771 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.703125 | 3 | CC-MAIN-2024-38 | latest | en | 0.906363 |
http://isle.illinois.edu/speech_web_lg/coursematerials/ece448/sp2021/assignment3.html | 1,670,118,964,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710953.78/warc/CC-MAIN-20221204004054-20221204034054-00214.warc.gz | 21,466,937 | 7,748 | ## Assignment 3: Neural Nets and PyTorch
### Due date: Wednesday March 17th, 11:59pm
image from Wikipedia
Created by Justin Lizama, Kedan Li, and Tiantian Fang
Updated fall 2020 by Jatin Arora, Kedan Li, and Michal Shlapentokh-Rothman
Updated spring 2021 by Mahir Morshed and Yangge Li
The goal of this assignment is to employ neural networks, nonlinear and multi-layer extensions of the linear perceptron, to detect whether or not images contain animals.
In the first part, you will create an 1980s-style shallow neural network. In the second part, you will improve this network using more modern techniques such as changing the activation function, changing the network architecture, or changing other initialization details.
You will be using the PyTorch and NumPy libraries to implement these models. The PyTorch library will do most of the heavy lifting for you, but it is still up to you to implement the right high-level instructions to train the model.
## Dataset
The dataset consists of 10000 32x32 colored images (a subset of the CIFAR-10 dataset, provided by Alex Krizhevsky), split for you into 7500 training examples (of which 2999 are negative and 4501 are positive) and 2500 development examples.
The data set can be downloaded here: (gzip) or (zip). When you uncompress this you'll find a binary object that our reader code will unpack for you.
## Part 1: Classical Shallow Network
The basic neural network model consists of a sequence of hidden layers sandwiched by an input and output layer. Input is fed into it from the input layer and the data is passed through the hidden layers and out to the output layer. Induced by every neural network is a function $$F_{W}$$ which is given by propagating the data through the layers.
To make things more precise, in lecture you learned of a function $$f_{w}(x) = \sum_{i=1}^n w_i x_i + b$$. In this assignment, given weight matrices $$W_1,W_2$$ with $$W_1 \in \mathbb{R}^{h \times d}$$, $$W_2 \in \mathbb{R}^{h \times 2}$$ and bias vectors $$b_1 \in \mathbb{R}^{h}$$ and $$b_2 \in \mathbb{R}^{2}$$, you will learn a function $$F_{W}$$ defined as $F_{W} (x) = W_2\sigma(W_1 x + b_1) + b_2$ where $$\sigma$$ is your activation function. In part 1, you should use either of the sigmoid or ReLU activation functions. You will use 32 hidden units ($$h=32$$) and 3072 input units, one for each channel of each pixel in an image ($$d=(32)^2(3) = 3072$$).
### Training and Development
• Training: To train the neural network you are going to need to minimize the empirical risk $$\mathcal{R}(W)$$ which is defined as the mean loss determined by some loss function. For this assignment you can use cross entropy for that loss function. In the case of binary classification, the empirical risk is given by $\mathcal{R}(W) = \frac{1}{n}\sum_{i=1}^n y_i \log \hat y_i + (1-y_i) \log (1 - \hat y_i) .$ where $$y_i$$ are the labels and $$\hat y_i$$ are determined by $$\hat y_i = \sigma(F_{W}(x_i))$$ where $$\sigma(x) = \frac{1}{1+e^{-x}}$$ is the sigmoid function. For this assignment, you won't have to implement these functions yourself; you can use the built-in PyTorch functions.
Notice that because PyTorch's CrossEntropyLoss incorporates a sigmoid function, you do not need to explicitly include an activation function in the last layer of your network.
• Development: After you have trained your neural network model, you will have your model decide whether or not images in the development set contain animals in them. This is done by evaluating your network $$F_{W}$$ on each example in the development set, and then taking the index of the maximum of the two outputs (argmax).
• Data Standardization: Convergence speed and accuracies can be improved greatly by simply centralizing your input data by subtracting the sample mean and dividing by the sample standard deviation. More precisely, you can alter your data matrix $$X$$ by simply setting $$X:=(X-\mu)/\sigma$$.
With the aforementioned model design and tips, you should expect around 0.84 dev-set accuracy.
## Part 2: Modern Network
In this part, you will try to improve your performance by employing more modern machine learning techniques. These include, but are not limited to, the following:
1. Choice of activation function: Some possible candidates include Tanh, ELU, softplus, and LeakyReLU. You may find that choosing the right activation function will lead to significantly faster convergence, improved performance overall, or even both.
2. L2 Regularization: Regularization is when you try to improve your model's ability to generalize to unseen examples. One commonly used form is L2 regularization. Let $$\mathcal{R}(W)$$ be the empirical risk (mean loss). You can implement L2 regularization by adding an additional term that penalizes the norm of the weights. More precisely, your new empirical risk becomes $\mathcal{R}(W):= \mathcal{R}(W) + \lambda \sum_{W \in P} \Vert W \Vert_2 ^2$ where $$P$$ is the set of all your parameters and $$\lambda$$ (usually small) is some hyperparameter you choose. There are several other techniques besides L2 regularization for improving the generalization of your model, such as dropout or batch normalization.
3. Network Depth and Width: The sort of network you implemented in part 1 is a two-layer network because it uses two weight matrices. Sometimes it helps performance to add more hidden units or add more weight matrices to obtain greater representation power and make training easier.
4. Using Convolutional Neural Networks: While it is possible to obtain nice results with traditional multilayer perceptrons, when doing image classification tasks it is often best to use convolutional neural networks, which are tailored specifically to signal processing tasks such as image recognition. See if you can improve your results using convolutional layers in your network.
Try to employ some of these techniques in order to attain an approximately 0.87 dev-set accuracy. The only stipulation is that you use under 500,000 total parameters. This means that if you take every floating point value in all of your weights including bias terms, you only use at most 500,000 floating point values.
### Some things to look for:
1. The autograder runs the training process for 500 batches (max_iter=500). This is done so that we have a consistent training process for each evaluation and comparison with benchmarks/threshold accuracies.
2. You still have one thing in your full control, however—the learning rate. In case you are confident about a model you implemented but are not able to pass the accuracy thresholds on gradescope, you can try increasing the learning rate. It is certainly possible that your model could do better with more training. Be mindful, however, that using a very high learning rate might deteriorate performance as well since the model may begin to oscillate around the optima.
## Provided Code Skeleton
We have provided (tar/zip) all the code to get you started on your MP, which means you will only have to implement the PyTorch neural network model.
• reader.py - This file is responsible for reading in the data set. It creates a giant NumPy array of feature vectors corresponding to each image.
• mp3.py - This is the main file that starts the program, and computes the accuracy, precision, recall, and F1-score using your implementation.
• neuralnet_part1.py and neuralnet_part2.py These are the files where you will be doing all of your work. You are given a NeuralNet class which implements a torch.nn.module. This class consists of __init__(), forward(), and step() functions. (Beyond the important details below, more on what each of these methods in the NeuralNet class should do is given in the skeleton code.)
• __init__() is where you will need to construct the network architecture. There are multiple ways to do this.
• One way is to use the Linear and Sequential objects. Keep in mind that Linear uses a Kaiming He uniform initialization to initialize the weight matrices and sets the bias terms to all zeros.
• Another way you could do things is by explicitly defining weight matrices W1, W2, ... and bias terms b1, b2, ... by defining them as Tensors. This approach is more hands on and will allow you to choose your own initialization. For this assignment, however, Kaiming He uniform initialization should suffice and should be a good choice.
Additionally, you can initialize an optimizer object in this function to use to optimize your network in the step() function.
• get_parameters() should do what its name suggests--namely, return a list of parameters used in the model. (This and set_parameters() will only be tested with respect to part 1, but you may find implementing and using these helpful for part 2.)
• set_parameters() should do what its name suggests--namely, set the parameters of the model based on those input to this method. For consistency's sake, the order of the parameters should be the same as those returned in get_parameters(). (This and get_parameters() will only be tested with respect to part 1, but you may find implementing and using these helpful for part 2.)
• forward() should perform a forward pass through your network. This means it should explicitly evaluate $$F_{W}(x)$$ . This can be done by simply calling your Sequential object defined in __init__() or (if you opted to define tensors explicitly) by multiplying through the weight matrices with your data.
• step() should perform one iteration of training. This means it should perform one gradient update through one batch of training data (not the entire set of training data). You can do this by either calling loss_fn(yhat,y).backward() then updating the weights directly yourself, or you can use an optimizer object that you may have initialized in __init__() to help you update the network. Be sure to call zero_grad() on your optimizer in order to clear the gradient buffer. When you return the loss_value from this function, make sure you return loss_value.item() (which works if it is just a single number) or loss_value.detach().cpu().numpy() (which separates the loss value from the computations that led up to it, moves it to the CPU—important if you decide to work locally on a GPU, bearing in mind that Gradescope won't be configured with a GPU—and then converts it to a NumPy array). This allows proper garbage collection to take place (lest your program possibly exceed the memory limits fixed on Gradescope).
• fit() takes as input the training data, training labels, development set, and the maximum number of iterations. The training data provided is the output from reader.py. The training labels is a Tensor consisting of labels corresponding to each image in the training data. The development set is the Tensor of images that you are going to test your implementation on. The maximium number of iterations is the number you specified with --max_iter (it is 500 by default). fit() outputs the predicted labels. It should construct a NeuralNet object, and iteratively call the neural net's step() to train the network. This should be done by feeding in batches of data determined by batch size. You will use a batch size of 100 for this assignment. max_iter is the number of batches (not the number of epochs!) in your training process.
The only files you will need to modify are neuralnet_part1.py and neuralnet_part2.py.
You should definitely use the PyTorch documentation, linked multiple times on this page, to help you with implementation details. You can also use this PyTorch Tutorial as a reference to help you with your implementation. There are also other guides out there such as this one.
## Deliverables
This MP will be submitted via Gradescope; please upload neuralnet_part1.py (for part 1) and neuralnet_part2.py (for part 2).
## Extra credit: CIFAR-100 superclasses
For an extra 10% worth of the points on this MP, your task will be to pick any two superclasses from the CIFAR-100 dataset (described in the same place as CIFAR-10) and rework your neural net from part 2, if necessary, to distinguish between those two superclasses. A superclass contains 2500 training images and 500 testing images, so between two superclasses you will be working with 3/5 the amount of data in total (6000 total images here versus 10000 total in the main MP).
You can download the CIFAR-100 data here and extract it to the same place where you've placed the data for the main MP. A custom reader for it is provided here; to use it with the CIFAR-100 data, you should rename this to reader.py and replace the existing file of that name in your working directory.
To set up your code for the extra credit, you must do the following:
• Note that your revised neural net must still have fewer than 500,000 total parameters.
• Define two variables class1 and class2 at the top level of the file containing your neural net (that is, outside of the NeuralNet class) to stand for indices representing superclasses from CIFAR-100. The order of the superclasses listed on the CIFAR description page hints at the index for each superclass; for example, "aquatic mammals" is 0 and "vehicles 2" is 19.
• Rename the file containing the neural net to submit to neuralnet.py. | 3,005 | 13,221 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.953125 | 3 | CC-MAIN-2022-49 | latest | en | 0.879738 |
https://www.dpreview.com/forums/post/53259200 | 1,472,082,358,000,000,000 | text/html | crawl-data/CC-MAIN-2016-36/segments/1471982292675.36/warc/CC-MAIN-20160823195812-00175-ip-10-153-172-175.ec2.internal.warc.gz | 914,248,641 | 17,322 | Reading mode: Light Dark
# How does a lens work to form an image on the camera's sensor...
Started Mar 7, 2014 | Discussions thread
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Re: How does a lens work to form an image on the camera's sensor...
1
You need a good primer on basic optics. The diagrams in these examples are next to useless.
The best explanation is to imagine how a lens would focus a single point, then two points, then all the points that make up a specific object.
Cameras capture light reflected off an object which radiates in all directions, including down your lens. If you imagine light streaming in straight lines from a given point, they will diverge. What a lens does is to refocus divergent rays to a single point....
In the diagrams above are three point objects. For simplicity only four of the billions of light rays from each object are shown.
In A the object is focused on the sensor. The curvature of the lens has the effect of bending light towards the centre of the lens (angle of refraction). However the angle through which it bends depends on the glass type (refractive index) and the curvature of the lens. If the distance from lens to sensor changes, the image will blur because the rays of light are not fully converged at the right point. (In this case I moved the sensor, in a camera you move the lens).
In B the closer object has rays which hit the lens at a steeper angle so they will not converge as quickly and will focus behind the sensor - the image will therefore be a blur covering all the points where light rays from that object hit. The further object will focus in front of the sensor, but the effect will be the same.
In C when you close down the aperture, you cut off the rays from the edges, so the blur radius also gets smaller and the objects appear sharper. Stop down more and they look sharper still (until diffraction starts to impact the overall sharpness). Effectively you are just using the centre part of the lens. Using a smaller lens would have the same effect. Of course, you also reduce the amount of light, so you need a longer exposure or higher ISO.
Please note most cameras have multiple elements in the lens, some which move and which don't. This so called compound lens corrects for the fact that (1) light of different wavelengths does not refract the same amount (chromatic aberration) and (2) that ground lenses do not focus exactly in the same point across the surface (spherical aberration). However a well corrected compound lens will combine multiple elements to get very close to a perfect lens. It also explains why aspherical elements are used in some complex lenses.
Hope that helps.
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Color scheme? Blue / Yellow | 623 | 2,871 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2016-36 | longest | en | 0.92997 |
https://blog.luz.vc/en/excel/how-to-do-curve-abc-in-excel/ | 1,623,710,704,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487613453.9/warc/CC-MAIN-20210614201339-20210614231339-00597.warc.gz | 143,008,047 | 38,789 | # How to Make ABC Curve in Excel
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The spreadsheet in Excel with the so-called ABC curve allows the user to make the inventory control your company. Through the data in this spreadsheet, the manager can make a comparison between the items and determine which ones are relevant and which are disposable for increasing the company's revenue.
Do not you know the ABC curve? You do not perform a comparison to control your stock? Know that using this tool is very important to reduce the costs of your business.
The origin of the ABC curve is a method based on theories of the Italian economist Vilfredo Pareto. It is about dividing the items of your stock into 3 groups according to their importance: A, B or C. In group A are the most important items. In group B are the intermediate level items. In group C are the items with low relevance.
## Stock management with the ABC curve in Excel
We elaborated a step by step how to make an ABC curve worksheet in Excel. Follow:
### Creating the 4 First Columns
Step 1: Initially we will create four columns and enter the values. Are they:
• First Column: A1-A11: It is the code of each product in your stock.
• Second Column: B1-B11: Quantity of product in stock.
• Third column: C1-C11: Unit value of each product.
• Fourth Column: D1-D11: Total value of the products.
Step 2: To complete the data in the fourth column, multiply the value of column B with the value of column C for the respective product. For example: To get the value of the D2 column, use the formula = B2 * C2. Therefore, the quantity of products multiplied by the unit value will result in the amount spent in your company for that stock item.
Step 3: After that, put the values in the D2 column in descending order.
Step 4: In sequence, in the D12 cell use the formula = SUM (D2: D11). The value will represent the amount of the amount spent in your company's current inventory.
### Inserting the%
Step 5: Create the% column in cell E1. The values of cells E2 through E11 represent the percentage that each value of Column D (cells D1 to D11) in relation to the value of cell D12.
Use the respective formulas in each cell below:
• Cell E2: = D2 / D12
• Cell E3: = D3 / D12
• Cell E4: = D4 / D12
• Cell E5: = D5 / D12
• Cell E6: = D6 / D12
• Cell E7: = D7 / D12
• Cell E8: = D8 / D12
• Cell E9: = D9 / D12
• Cell E10: = D10 / D12
• Cell E11: = D11 / D12
Step 6: After that, select the E2 cells up to E11 and click Home / Number /%.
Step 7: In sequence, in the E12 cell use the formula = SUM (E2: E11). If the result is 100%, the worksheet is correct until now. Otherwise, check the step-by-step again to notice the error and correct the error.
### Inserting% Accumulated column
Step 8: Create the% Accumulated column in the F1 cell. The values of the F2 cells to F11 represent the sum of the percentages of the% column.
Use the respective formulas in each cell below:
• F2 cell: = E2
• F3 cell: = F2 + E3
• F4 cell: = F3 + E4
• F5 cell: = F4 + E5
• F6 cell: = F5 + E6
• F7 cell: = F6 + E7
• F8 cell: = F7 + E8
• F9 cell: = F8 + E9
• F10 cell: = F9 + E10
• F11 cell: = F10 + E11
Step 9: Once this is done, select cells F2 through F11 and click Home / Number /%.
### Inserting the graph with the ABC curve
Step 10: Select the values of the A2 cells up to A11.
Step 11: Holding down the CTRL key also select the values of the F2 cells to F11.
Step 12: Select the chart: Insert / Graph / Rows / Line 2d / Rows.
Step 13: Select the 1 Series caption and then click DELETE.
Step 14: The percentage axis is between 0 and 120%. To leave between the values of 0 and 100% select the axis and click on Format axis.
Step 15: In axis options, select FIXED for minimum and maximum. Respectively leave them at 0,0 and 1,0. Click CLOSE.
Through these steps the worksheet will be ready. You can change colors and leave it any way you like.
## Analyzing the spreadsheet data with ABC curve
Taking into account 3 groups A, B and C, we chose the reference 70-20-10.
That way group A represents 70% of total costs, group B 20%, and group 10%.
Taking into account the data of this worksheet, the groups are represented:
• GROUP A: 3 products (9, 4 and 10 codes);
• GROUP B: 2 products (5 and 8 codes);
• GROUP C: 5 products (1, 3, 6, 7 and 2 codes).
Therefore:
• 30% of products represent 70% of total costs;
• 20% of products represent 20% of total costs;
• 50% of products represent 10% of total costs.
This data is of fundamental importance for you to maintain a controlled inventory and perform an adequate management for perfect investments.
Administrator and turismologist, passionate about the possibilities that Excel gives to managers, entrepreneurs and students. He is the managing partner of the spreadsheet department at LUZ - Spreadsheets (luz.vc) and is responsible for the development of spreadsheets with business and personal focus commercialized in its website. He also teaches online Excel courses (cursos.luz.vc) and likes to help thousands of planners through the LUZ Forum and Blog.
1. You're welcome, Claudio! Hugs and any other questions I am at your disposal.
2. No problem, they are approximate values. When defining the cuts you will have to make a decision, whether you want to pick up to the last value before the cut values (70 - 20 - 10) or the next value
3. Is Cesar talking, is everything okay? Let's do it by steps:
1 - To make the third column, just take the values of the accumulated percentages (column F), see that in the third product (quantity of type A) we have approximately 70%. To find this value you can do a VLOOKUP (I would create an initial auxiliary column with the numbering of the quantity of products (1, 2, 3, 4, etc.) and use the PRODUCTS column of the auxiliary table to find the corresponding percentage.
2 - The% of total products is even simpler, just make a CONT of the total quantity of products and make a simple division of the quantity of products in a certain group (A, B or C) by this total.
3 - The colors of the lines are a little more complicated. I don't really remember how it was done, but I believe that he inserted three series of data in the graph, each series looking for the accumulated percentage values for each group and then changed the color of each of the lines - particularly I don't think that make the graph more explanatory ...
4. Hi, I have a problem with 70-20, but I can not get the 10-2 reference table. columns, the first one I used the function Cont.se and it worked, already the other columns neither I have idea, and also how to paint the lines of the graph in the same way as in the article?
Thank you very much in advance!
5. it was necessary to place the region below the filled curve to be 10 = v
6. I'm making an ABC curve using an autofilter table, I wonder if you know any formula that calculates the percentage accumulated when the filter is applied.
7. Could you explain how this second table does and how do you determine these colored ABC lines?
Thank you
8. good afternoon,
how do I get the values in the last column of the second table,% total products?
9. Hi Bruno, to do this calculation it is necessary to put the values in descending order in a column and make the accumulated of each successively in another.
So you get what it represents in% and how much the accumulated represents. From there, just think of the percentages and establish the criteria of which groups A, B and C are
10. Hi Mineirinho, how are things good?
If you want to improve your Excel skills, we have two very good online courses that can help you a lot! One is a beginner / intermediate and the other advanced. You can find out more about them (and even see some free classes) at this link - http://cursos.luz.vc/ | 1,977 | 7,775 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.84375 | 4 | CC-MAIN-2021-25 | latest | en | 0.897579 |
http://mathsframe.co.uk/en/resources/category/87/year_4_block_a_use_knowledge_of_addition_and_subtraction_facts_and_place_value_to_derive_sums_and_differences_of_pairs_of_multiples_of_10_100_or_1000 | 1,488,398,671,000,000,000 | text/html | crawl-data/CC-MAIN-2017-09/segments/1487501174276.22/warc/CC-MAIN-20170219104614-00540-ip-10-171-10-108.ec2.internal.warc.gz | 158,013,168 | 33,176 | # Use knowledge of addition and subtraction facts and place value to derive sums and differences of pairs of multiples of 10, 100 or 1000
Subtraction - Crystal Crash
The game was designed to cover all the mental subtraction objectives in the new math curriculum. You can choose one objective, or choose all the objectives for a year group.
This game, together with all the other crystal crash games, is available as a single iPad or Android app.
1) Subtract numbers from up to 10 (Y1) 6) Subtract from 100 (multiples of 10) (Y3) 11) Subtract tens from a three-digit number (Y3) 16) Subtract combinations of decimals (1dp) (Y4) 2) Subtract numbers from up to 20 (Y1) 7)Subtract from 100 (multiples of 5) (Y3) 12) Subtract hundreds from a three-digit number (Y3) 17) Subtract a decimal (2dp) from 1 (Y5 & Y6) 3) Subtract ones from a two-digit number (Y2) 8) Subtract from 100 (Y3 & Y4) 13) Subtract a decimal (1dp) from 1 (Y4 & Y5) 18) Subtract combinations of three-digit numbers (Y5 & Y6) 4) Subtract tens from a two-digit number (Y2) 9) Subtract from 1000 (multiples of 100) (Y3 & Y4) 14) Subtract a decimal (1dp) from 10 (Y4 & Y5) 19) Subtract combinations of decimals (2dp) (Y5 & Y6) 5) Subtract a two-digit number from a two-digit number (Y2) 10) Subtract ones from a three-digit number(Y3) 15) Subtract two-digit numbers from three-digit numbers (y4)
Balance scales - add, move or remove a weight
Balance the scales by adding, moving or removing a weight. A great mental starter to develop addition and subtraction skills.
A fun game to practise mental addition skills. The game was designed to cover all the mental addition objectives in the new math curriculum. You can choose one objective, or choose all the objectives for a year group.
This game, together with all the other crystal crash games, is available as a single iPad or Android app.
Balancing Sums
An excellent tool for reinforcing an understanding of the role of the equals sign. Choose one objective, or many. You can choose all the objectives for a single year group (or multiple year groups). You can also choose to balance between different types of calculations (eg addition and multiplication).
Bubble Pop - Number Bonds
A great way to practise number bonds and mental addition. Levels include: number bonds to 10, 20, 50 and 100 as well as addition pairs with a total of up to 20, 50 or 100. Look at the target at the top of the screen and then aim your bubble to make that target.
As a teacher I know how important it is that children know their number bonds (pairs of numbers that add up to 10, 20, 50 or 100), and can add quickly mentally. Repetition is essential in learning number bonds. This game is designed to make the process fun.
Children have to aim their bubble to make a given sum. As they progress the levels get harder; they have less time, or less bubbles to shoot. Each correct answer is accompanied by an image to reinforce the number bond they have found.
This game is available on iPad, iPod and iPhone, as well as on android phones and tablets.
Missing Symbols
Drag the symbols to the correct position to make the number sentence correct. Lots of levels to play. See if you can improve your score over time.
This game is now part of the 'Calculations' collection, which includes the following 17 games and resources: Column Addition, Expanded Addition, Expanded Addition - Place Value Counters, Number Bonds(2), Addition - Digit Drag, Missing Symbols, Column Subtraction, Column Subtraction using Place Value Counters, Counting on to find difference on a beadstring, Multiplication Grid Method, Multiplication Written Method, Ratio and Scaling Numbers, Representing Multiplication, Division by Chunking Up, Division by Chunking Down, Formal Written Division - Round Up or Down?, Short Division Writen Formal Method.
The Calculations app is available on Google Play and the App Store.
Number Facts Beat The Clock
Score as many points as you can before the time runs out. A number of levels including addition, subtraction, multiplication, division and matching fractions and decimals.
*Updated 30th May 2013 - choose multiple objectives, or objectives grouped by national curriculum level. The game also now includes a scoreboard. An iPad version is also available.
Ordering Calculations
Order the calulations from those with the least value to the greatest. Lots of levels, including; addition pairs to 20, addition pairs to 100, addition and subtraction of multiples of 10, and multiplication of numbers up to 10. | 1,072 | 4,537 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.578125 | 4 | CC-MAIN-2017-09 | latest | en | 0.783586 |
https://www.askthebuilder.com/electrical-shock-touching-light-fixture/?awt_l=Mrjqc&awt_m=I_pSHEC5MbNiL5 | 1,516,268,970,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084887224.19/warc/CC-MAIN-20180118091548-20180118111548-00123.warc.gz | 912,294,690 | 18,270 | # Electrical Shock Touching Light Fixture
Quick Column Summary:
• Shock from 3 way switch
• Why this happens
• Locate the bare wire
William Roberts from Orlando, Florida (FL) wrote to me:
"I have a three way switched light - like the example in your garden shed video.
Both switches work correctly, but if I touch the light fixture when the light is on, I get shocked.
What would be the cause of that?"
Well William, that's easy. The fixture is becoming energized by the electric current in the circuit. I put that video you watched below for you.
You gave a clue to the source of the problem when you said this only happens when the light is ON.
Here's what's going on.
When you have an alternating current circuit in the OFF situation where NO CURRENT is flowing, the white or neutral wire is the same as the bare ground wire. This means you can touch the white wire and not get shocked.
But, when you have current flowing in the circuit, a light on, the toaster coils glowing red, the wet-dry vacuum on, the computer on, etc., the white wire in the circuit becomes ENERGIZED. The HOT part of the electricity starts to move back and forth along the white wire.
This is why it's called alternating current. The alternating current in your home cycles at 60 times per second. The electrons in the black and white wires move back and forth along the wires about two feet or so constantly reversing direction - 60 times per second. If the current was direct, the electrons would march from one end of the wire to another like water flows through your garden hose.
I discovered that white wires in a circuit can become energized 35 years ago when I grabbed onto what I thought was a SAFE bare end of a bunch of white wires and was thrown from the ladder by the vigorous JOLT of the alternating current. Had the circuit breaker been turned OFF, I could have touched the white wires and nothing happened.
You need to locate where a nicked or bare part of the white wires in the fixture is touching the metal of the fixture.
If you were to get shocked touching the fixture all the time - even when the light is OFF - that means the black, or HOT, wire is what's touching the metal in the fixture.
## 4 Responses to Electrical Shock Touching Light Fixture
1. John Perodeau says:
Could it not also be that the black and wires wires are reversed somewhere?
2. Edward says:
I thought you should switch the hot (black) wire for this reason. The light hot line should be switched on and off. The black wire from the circuit breaker should go to the common of one of the switches, the light hot goes to the common of the other switch. the 2 poles of the switches connect to eachother . The only white wire that would be live would be going to a(nother) light switch. In that case a piece of black tape should be wrapped around the white wire to indicate it could be hot.
3. Mike Collins says:
Tim,
Brilliant three-way switch video!
Mike
4. Lou Herrick says:
Dear Tim,
I have to disagree with your conclusion; if the writer got shocked while he was standing on the ground, pavement, etc. and touched the body of the fixture, this means that the body of the fixture was not grounded per NEC. If it was, as soon as the light was turned ON, the black wire would be shorted to ground, tripping the breaker.
Also, even though the white wire (neutral) is carrying current, unless it is an extremely long circuit, it is effectively at ground potential, and you will not be shocked – no more so than if you touched the same neutral wire where it is bonded to the panel ground bus. | 786 | 3,588 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.171875 | 3 | CC-MAIN-2018-05 | latest | en | 0.955903 |
https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327-380.html | 1,537,649,919,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267158691.56/warc/CC-MAIN-20180922201637-20180922222037-00476.warc.gz | 523,281,001 | 54,566 | GMAT Question of the Day - Daily to your Mailbox; hard ones only
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# How to get 6.0 AWA....my guide
Author Message
Intern
Joined: 15 Mar 2015
Posts: 13
Concentration: Operations, Strategy
GMAT 1: 550 Q35 V30
WE: Operations (Manufacturing)
Re: How to get 6.0 AWA....my guide [#permalink]
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27 Apr 2016, 11:32
I just received my AWA score and I got a 6 by using this template. Excellent guide and really helpful in echoing what others have said in regards to using the template to eliminate the guesswork and save mental energy for the quant and verbal portions of the test. Highly recommend this to anyone that struggles with writing cohesively. I am normally a strong essay writer, but this guide helped tremendously in structuring on-the-fly.
+1
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Re: How to get 6.0 AWA....my guide [#permalink]
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27 Apr 2016, 23:29
Thanks a lot! Your post is brilliant and helped me get a 6 on the essay. The structure allowed me to present my reasoning without struggling to create a cohesive whole.
Really appreciate you posting the structure in this forum and helping others who are planning to give their GMAT.
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Re: How to get 6.0 AWA....my guide [#permalink]
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03 May 2016, 13:04
1
How to Prepare for the GMAT Essay Section
Try to make the most of the time you have to prepare for the GMAT Analytical Writing Assessment (the GMAT essay section). Write practice essays under exam conditions, take notes on a variety of official essay topics, and exploit resources such as my two GMAT essay books. This page provides details about each strategy.
Practice, Practice and More Practice
You could study many "model" GMAT essays and review every available essay-writing tip, yet still perform poorly on the actual exam. That's because there’s no substitute for putting yourself to the task under simulated exam conditions.
Compose as many practice essays as you reasonably have time for, responding to the official GMAT essay prompts. In so doing:
Always practice under timed conditions. Unless you're put under the pressure of time, you really won’t be ready for the test.
Always use a word processor for your practice tests. Be sure to use only the GMAT word processor's limited editing functions.
Evaluate your practice essays. Practicing isn’t all that helpful if you make the same blunders again and again. After composing an essay, evaluate and score it based on the official criteria. Then reflect on your weaknesses and concentrate on improving in those areas the next time. Don’t worry if you don’t produce perfect models. Concentrate instead on improving your performance next time.
Take Notes on a Variety of Official Essay Prompts
From the official GMAT website download the current list of Argument Analysis prompts. Select any 10-15 Arguments. For each one, spend about 5 minutes brainstorming and making notes. Even if none of the prompts you selected appears on your exam, this exercise will go a long way toward ensuring that you don't find yourself paralyzed, or stuck, during the actual exam.
My book GMAT—Answers to the Real Essay Questions (published by Peterson's) contains sample essays for more than a hundred GMAT Argument Analysis prompts. Randomly select from Part 3 as many essays as you reasonably have time to study. For each essay:
Identify the types of reasoning problems that the essay discusses and that you learned about in Part 1 of the book.
Highlight transition phrases, which connect the essay's points of critique. Then make a special effort to incorporate similar phrases into your practice essays.
CAVEAT: Don’t try to memorize the book's sample essays. GMAT readers are familiar with the book and will recognize plagiarism when they see it. There’s nothing wrong with borrowing ideas, reasons and transition phrases from the book's sample essays. Do try, however, to include your own specific examples. And be sure to express your ideas in your own words.
If your analytical-writing skills need significant improvement, further help is available in my book Writing Skills for the GRE-GMAT (also published by Peterson's). The book places special emphasis on building rhetorical writing skills, organizing your GMAT essay, and avoiding or correcting common language, grammar and mechanical problems.
The book also explores additional (less frequent) reasoning problems with Arguments in the official pool. Finally, to help improve and polish your analytic and writing skills, the book contains a variety of reinforcement exercises for the Argument Analysis writing task.
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Joined: 17 Jul 2014
Posts: 2683
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
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Re: How to get 6.0 AWA....my guide [#permalink]
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07 May 2016, 10:54
I got perfect score on AWA thanks to chineseburned!!!!
really incredible post!!!
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Joined: 08 Apr 2016
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GMAT 1: 770 Q50 V45
Re: How to get 6.0 AWA....my guide [#permalink]
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12 May 2016, 01:28
Brilliant! I also got a 6.0 thanks to this post
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Posts: 6
Re: How to get 6.0 AWA....my guide [#permalink]
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17 Jun 2016, 17:26
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Best guide if you want to get 6 AWA score.
Thanks
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Posts: 5
Re: How to get 6.0 AWA....my guide [#permalink]
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20 Jul 2016, 06:06
Wow, didn't do one practice essay (ill-advised; was short on time), but still managed to get a 6.0/6.0 on the writing thanks to this. WOW, it is almost like cheating! Amazing, thank you!
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Re: How to get 6.0 AWA....my guide [#permalink]
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21 Jul 2016, 09:16
*just hypothesizing*
Guys, don't you think that adcom could penalise for such "tricks" if they check out one's essay? Say a bunch of people applying to HBS; clearly, the majority took a look on this topic/forum. Then there is a high probability this applicants would follow the same template. So HBS would see a lot of similar essays, and that's not good IMO.
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Re: How to get 6.0 AWA....my guide [#permalink]
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21 Jul 2016, 16:00
1
manlog wrote:
*just hypothesizing*
Guys, don't you think that adcom could penalise for such "tricks" if they check out one's essay? Say a bunch of people applying to HBS; clearly, the majority took a look on this topic/forum. Then there is a high probability this applicants would follow the same template. So HBS would see a lot of similar essays, and that's not good IMO.
Good point! To me, the problem lies with the GMAT scoring system. There is no reason quality/content couldn't be scored in a fair manner; see APLAC's and AP Lit's 9 point scale as needed. From an ADCOM's/prospective student's perspective, it seems to be a student would be dumb to have known about a template that seemingly guarantees him or her a 6 and not use it. Thus, I don't think an ADCOM can see it in any other way than that the student was resourceful, which is probably good, but at worst I think they just call it a draw and it doesn't really help/hurt you. From my understanding, the main time they care about the AWA score is when they have questions about the authenticity of who wrote the application essays. If you write those genuinely, I doubt there will be any issue. Definitely a fair point to raise, though.
It is also probably worth noting that this template has been around for 8 years and there are no reports of it being an issue (to my knowledge).
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Re: How to get 6.0 AWA....my guide [#permalink]
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29 Aug 2016, 12:19
Best guide for AWA. I am non-native speaker and I practiced AWA couple days before the exam and I followed this guide and I got 6.0/ 90%ile on my exam.
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01 Sep 2016, 03:47
so great!
help a lot !
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12 Sep 2016, 16:25
Thanks Mate. This post is really helpful.
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Re: How to get 6.0 AWA....my guide [#permalink]
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30 Sep 2016, 07:41
Thank you so much for this guide! Just got my official GMAT score today and I scored 6.0 on AWA thanks to this guide!! I strictly stuck to this guide and it really paid off for me!
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Re: How to get 6.0 AWA....my guide [#permalink]
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01 Oct 2016, 03:44
Good day all.
Thanks Chineseburned for awesome material.
I have my GMAT in Decemeber and i need more practice in AWA. Taking into account that this forum is extremelly full of 6-graders i
want to ask you guys for little help. Could you please shortly comment on any mistakes and inconsistencies in my AWA essay written by abovementioned template:
PROMT:
“When the Apogee Company had all its operations in one location, it was more profitable
than it is today. Therefore, the Apogee Company should close down its field offices and
conduct all its operations from a single location. Such centralization would improve
profitability by cutting costs and helping the company maintain better supervision of all
employees.”
ANALYSIS OF AN ARGUMENT:
The argument claims that closing of all field offices will make Apogee Company more profitable
through costs cutting and increase in level of control. Supporting evidence of an argument is that Apogee Company
was more profitable when it had all operations in one office. Stated in this way the argument fails to mention several
key factors on the basis of which it could be evaluated. Evidence cited is not solid, argument is unconvincing and
has several flaws.
First the argument readily assumes that opening of new offices is the only reason for profitability reduction and draws
from this assumtion unreasonable conclusion that offices should be cloused down. However there could be a banch of reasons.
For example, wrong places could have been chosen for new offices with no preliminary analysis performed. In such case more logical decision would be conduction of in depth pre analysis and relocation of offices in accordance with its results. Other
possible reasons could be influence of external economical factors on core business of the Company or plethora of internal
factors increasing Company's expenditures, such as implementation of other major investment projects at the same time with
openning new offices. Therefore decision on closing of new offices can not be made solely based on deacrease of profitability level and requires full knowledge of all contributing factos. If the argument had provided explicit evidence that opening new offices is the only reason for profit decrease then the argument would have been a lot more convincing.
Second the argument claims that centralization would improve profitability by cutting costs and better supervision of employees.
While centralization may improve profitability in short time perspective and enhance internal supervision of employees, but it will definitely inhibit Company's growth by blocking entry to new markets and regions. Openning of new offices is a serious strategic initiative which leads to profitability reduction in short time perspective due to increase in related expenditures (construction/rent of office buildings, logistics and etc.) and is usually directed at company's growth and profitability increase in the long run. Besides, it is clear that some time is required for new offices to start operations at full capacity, attract new clients and achieve payback. The argument could have been much clearer if it stated that there was no profit increase or that there was steady profit decrease during reasonable time period of Company's operations with new offices. Without reference to the time period, the argument remains unsubstantiated and open to debate.
In conclusion, the argument is flawed for the above-mentioned reasons and is therefore unconvincing. It could be considerably strengthened if the author clearly mentioned all the relevant facts.
Intern
Joined: 22 Jun 2016
Posts: 3
Re: How to get 6.0 AWA....my guide [#permalink]
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01 Oct 2016, 03:51
Good day all.
Thanks for awesome material.
I have my GMAT in December and so need more practice in AWA. Taking into account that this place is full of 6-graded i want to ask you guys for a little help. Could you please provide your comments of my AWA essay (see below). Thank you in advance!
PROMT:
“When the Apogee Company had all its operations in one location, it was more profitable
than it is today. Therefore, the Apogee Company should close down its field offices and
conduct all its operations from a single location. Such centralization would improve
profitability by cutting costs and helping the company maintain better supervision of all
employees.”
ANALYSIS OF AN ARGUMENT:
The argument claims that closing of all field offices will make Apogee Company more profitable
through costs cutting and increase in level of control. Supporting evidence of an argument is that Apogee Company
was more profitable when it had all operations in one office. Stated in this way the argument fails to mention several
key factors on the basis of which it could be evaluated. Evidence cited is not solid, argument is unconvincing and
has several flaws.
First the argument readily assumes that opening of new offices is the only reason for profitability reduction and draws
from this assumtion unreasonable conclusion that offices should be cloused down. However there could be a banch of reasons.
For example, wrong places could have been chosen for new offices with no preliminary analysis performed. In such case more logical decision would be conduction of in depth pre analysis and relocation of offices in accordance with its results. Other
possible reasons could be influence of external economical factors on core business of the Company or plethora of internal
factors increasing Company's expenditures, such as implementation of other major investment projects at the same time with
openning new offices. Therefore decision on closing of new offices can not be made solely based on deacrease of profitability level and requires full knowledge of all contributing factos. If the argument had provided explicit evidence that opening new offices is the only reason for profit decrease then the argument would have been a lot more convincing.
Second the argument claims that centralization would improve profitability by cutting costs and better supervision of employees.
While centralization may improve profitability in short time perspective and enhance internal supervision of employees, but it will definitely inhibit Company's growth by blocking entry to new markets and regions. Openning of new offices is a serious strategic initiative which leads to profitability reduction in short time perspective due to increase in related expenditures (construction/rent of office buildings, logistics and etc.) and is usually directed at company's growth and profitability increase in the long run. Besides, it is clear that some time is required for new offices to start operations at full capacity, attract new clients and achieve payback. The argument could have been much clearer if it stated that there was no profit increase or that there was steady profit decrease during reasonable time period of Company's operations with new offices. Without reference to the time period, the argument remains unsubstantiated and open to debate.
In conclusion, the argument is flawed for the above-mentioned reasons and is therefore unconvincing. It could be considerably strengthened if the author clearly mentioned all the relevant facts.
Current Student
Joined: 28 Aug 2016
Posts: 90
Concentration: Strategy, General Management
Re: How to get 6.0 AWA....my guide [#permalink]
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01 Oct 2016, 13:36
Postol91 wrote:
Good day all.
Thanks for awesome material.
I have my GMAT in December and so need more practice in AWA. Taking into account that this place is full of 6-graded i want to ask you guys for a little help. Could you please provide your comments of my AWA essay (see below). Thank you in advance!
PROMT:
“When the Apogee Company had all its operations in one location, it was more profitable
than it is today. Therefore, the Apogee Company should close down its field offices and
conduct all its operations from a single location. Such centralization would improve
profitability by cutting costs and helping the company maintain better supervision of all
employees.”
ANALYSIS OF AN ARGUMENT:
The argument claims that closing of all field offices will make Apogee Company more profitable
through costs cutting and increase in level of control. Supporting evidence of an argument is that Apogee Company
was more profitable when it had all operations in one office. Stated in this way the argument fails to mention several
key factors on the basis of which it could be evaluated. Evidence cited is not solid, argument is unconvincing and
has several flaws.
First the argument readily assumes that opening of new offices is the only reason for profitability reduction and draws
from this assumtion unreasonable conclusion that offices should be cloused down. However there could be a banch of reasons.
For example, wrong places could have been chosen for new offices with no preliminary analysis performed. In such case more logical decision would be conduction of in depth pre analysis and relocation of offices in accordance with its results. Other
possible reasons could be influence of external economical factors on core business of the Company or plethora of internal
factors increasing Company's expenditures, such as implementation of other major investment projects at the same time with
openning new offices. Therefore decision on closing of new offices can not be made solely based on deacrease of profitability level and requires full knowledge of all contributing factos. If the argument had provided explicit evidence that opening new offices is the only reason for profit decrease then the argument would have been a lot more convincing.
Second the argument claims that centralization would improve profitability by cutting costs and better supervision of employees.
While centralization may improve profitability in short time perspective and enhance internal supervision of employees, but it will definitely inhibit Company's growth by blocking entry to new markets and regions. Openning of new offices is a serious strategic initiative which leads to profitability reduction in short time perspective due to increase in related expenditures (construction/rent of office buildings, logistics and etc.) and is usually directed at company's growth and profitability increase in the long run. Besides, it is clear that some time is required for new offices to start operations at full capacity, attract new clients and achieve payback. The argument could have been much clearer if it stated that there was no profit increase or that there was steady profit decrease during reasonable time period of Company's operations with new offices. Without reference to the time period, the argument remains unsubstantiated and open to debate.
In conclusion, the argument is flawed for the above-mentioned reasons and is therefore unconvincing. It could be considerably strengthened if the author clearly mentioned all the relevant facts.
I would add one more paragraph before the conclusion as mentioned in this guide. I did the same for my AWA as well. In the third paragraph, list a couple of things that were failed to be mentioned in the argument and can be added to strengthen it.
You are also missing a lot of commas. After First, Second... after Stated in this way... Some of the idioms are wrong, such as While... But which do not go together. I also wouldn't use parenthesis and etc.
Overall, it seems like you have to work on improving your writing style and skills first. Put more time into studying verbal section, as it helped me tremendously to improve my grammatical skills. I also recommend that you enroll in a course where you can practice your writing and can obtain proper feedback.
Good luck.
Intern
Joined: 22 Jun 2016
Posts: 3
Re: How to get 6.0 AWA....my guide [#permalink]
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02 Oct 2016, 03:03
Rookie84 wrote:
Postol91 wrote:
Good day all.
Thanks for awesome material.
I have my GMAT in December and so need more practice in AWA. Taking into account that this place is full of 6-graded i want to ask you guys for a little help. Could you please provide your comments of my AWA essay (see below). Thank you in advance!
PROMT:
“When the Apogee Company had all its operations in one location, it was more profitable
than it is today. Therefore, the Apogee Company should close down its field offices and
conduct all its operations from a single location. Such centralization would improve
profitability by cutting costs and helping the company maintain better supervision of all
employees.”
ANALYSIS OF AN ARGUMENT:
The argument claims that closing of all field offices will make Apogee Company more profitable
through costs cutting and increase in level of control. Supporting evidence of an argument is that Apogee Company
was more profitable when it had all operations in one office. Stated in this way the argument fails to mention several
key factors on the basis of which it could be evaluated. Evidence cited is not solid, argument is unconvincing and
has several flaws.
First the argument readily assumes that opening of new offices is the only reason for profitability reduction and draws
from this assumtion unreasonable conclusion that offices should be cloused down. However there could be a banch of reasons.
For example, wrong places could have been chosen for new offices with no preliminary analysis performed. In such case more logical decision would be conduction of in depth pre analysis and relocation of offices in accordance with its results. Other
possible reasons could be influence of external economical factors on core business of the Company or plethora of internal
factors increasing Company's expenditures, such as implementation of other major investment projects at the same time with
openning new offices. Therefore decision on closing of new offices can not be made solely based on deacrease of profitability level and requires full knowledge of all contributing factos. If the argument had provided explicit evidence that opening new offices is the only reason for profit decrease then the argument would have been a lot more convincing.
Second the argument claims that centralization would improve profitability by cutting costs and better supervision of employees.
While centralization may improve profitability in short time perspective and enhance internal supervision of employees, but it will definitely inhibit Company's growth by blocking entry to new markets and regions. Openning of new offices is a serious strategic initiative which leads to profitability reduction in short time perspective due to increase in related expenditures (construction/rent of office buildings, logistics and etc.) and is usually directed at company's growth and profitability increase in the long run. Besides, it is clear that some time is required for new offices to start operations at full capacity, attract new clients and achieve payback. The argument could have been much clearer if it stated that there was no profit increase or that there was steady profit decrease during reasonable time period of Company's operations with new offices. Without reference to the time period, the argument remains unsubstantiated and open to debate.
In conclusion, the argument is flawed for the above-mentioned reasons and is therefore unconvincing. It could be considerably strengthened if the author clearly mentioned all the relevant facts.
I would add one more paragraph before the conclusion as mentioned in this guide. I did the same for my AWA as well. In the third paragraph, list a couple of things that were failed to be mentioned in the argument and can be added to strengthen it.
You are also missing a lot of commas. After First, Second... after Stated in this way... Some of the idioms are wrong, such as While... But which do not go together. I also wouldn't use parenthesis and etc.
Overall, it seems like you have to work on improving your writing style and skills first. Put more time into studying verbal section, as it helped me tremendously to improve my grammatical skills. I also recommend that you enroll in a course where you can practice your writing and can obtain proper feedback.
Good luck.
Intern
Joined: 03 Oct 2016
Posts: 7
Re: How to get 6.0 AWA....my guide [#permalink]
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03 Oct 2016, 11:19
Intern
Joined: 04 Sep 2014
Posts: 1
Re: How to get 6.0 AWA....my guide [#permalink]
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06 Oct 2016, 13:11
Thank you so much. I read through an entire GMAT Princeton review text-book. Everything you stated in this post, is exactly what I found in the book. You rock!!!
Intern
Joined: 26 Aug 2010
Posts: 1
Re: How to get 6.0 AWA....my guide [#permalink]
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08 Oct 2016, 17:27
Excellent !! Very informative and helpful
Re: How to get 6.0 AWA....my guide &nbs [#permalink] 08 Oct 2016, 17:27
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# 51 Results
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Students will find the perimeter of a hexagonal region.
Subject:
Mathematics
Material Type:
Lesson Plan
Author:
Drew Polly
07/12/2020
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Four full-year digital course, built from the ground up and fully-aligned to the Common Core State Standards, for 7th grade Mathematics. Created using research-based approaches to teaching and learning, the Open Access Common Core Course for Mathematics is designed with student-centered learning in mind, including activities for students to develop valuable 21st century skills and academic mindset.
Subject:
Mathematics
Material Type:
Full Course
Provider:
Pearson
11/02/2020
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Algebraic Reasoning
Type of Unit: Concept
Prior Knowledge
Students should be able to:
Add, subtract, multiply, and divide rational numbers.
Evaluate expressions for a value of a variable.
Use the distributive property to generate equivalent expressions including combining like terms.
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true?
Write and solve equations of the form x+p=q and px=q for cases in which p, q, and x are non-negative rational numbers.
Understand and graph solutions to inequalities x<c or x>c.
Use equations, tables, and graphs to represent the relationship between two variables.
Relate fractions, decimals, and percents.
Solve percent problems included those involving percent of increase or percent of decrease.
Lesson Flow
This unit covers all of the Common Core State Standards for Expressions and Equations in Grade 7. Students extend what they learned in Grade 6 about evaluating expressions and using properties to write equivalent expressions. They write, evaluate, and simplify expressions that now contain both positive and negative rational numbers. They write algebraic expressions for problem situations and discuss how different equivalent expressions can be used to represent different ways of solving the same problem. They make connections between various forms of rational numbers. Students apply what they learned in Grade 6 about solving equations such as x+2=6 or 3x=12 to solving equations such as 3x+6=12 and 3(x−2)=12. Students solve these equations using formal algebraic methods. The numbers in these equations can now be rational numbers. They use estimation and mental math to estimate solutions. They learn how solving linear inequalities differs from solving linear equations and then they solve and graph linear inequalities such as −3x+4<12. Students use inequalities to solve real-world problems, solving the problem first by arithmetic and then by writing and solving an inequality. They see that the solution of the algebraic inequality may differ from the solution to the problem.
Subject:
Algebra
Mathematics
Provider:
Pearson
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Students write expressions for geometric situations. They examine how different equivalent expressions can show different ways of thinking about the same problem.Key ConceptsStudents use their previous knowledge of how to find the perimeter and area of squares and rectangles. They write algebraic expressions for the perimeter and area of geometric figures. They examine how equivalent expressions, used to represent a problem situation, give clues to the approach the writer of the expression used to solve the problem. In the Challenge Problem, they use the distributive property to find the solution.ELL: For ELLs, access prior knowledge by writing the words area and perimeter on the board. Have students create concept maps associated with area and perimeter. Record students' responses on large poster paper that you can display in the room. The goal is to generate a list of words that students can use as a reference.Goals and Learning ObjectivesAccess prior knowledge of how to find the perimeter and area of squares and rectangles.Write algebraic expressions for finding perimeter or area of figures.Identify equivalent expressions.
Subject:
Geometry
Material Type:
Lesson Plan
Author:
Pearson
11/02/2020
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This resource is from Tools 4 NC Teachers. This document is the About the Cluster document for Cluster 6 created by the authors of the NC2ML Instructional Frameworks. This document should be read prior to teaching Cluster 6. This document is not remixable since the document has been written by creators of the NC2ML Instructional Frameworks.
Subject:
Mathematics
Material Type:
Reference Material
07/07/2019
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This short video and interactive assessment activity is designed to teach third graders about perimeter in grid.
Subject:
Mathematics
Material Type:
Assessment
Interactive
Lecture
Provider:
CK-12 Foundation
Provider Set:
CK-12 Elementary Math
06/06/2019
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This short video and interactive assessment activity is designed to teach third graders about perimeter of squares and rectangles.
Subject:
Mathematics
Material Type:
Assessment
Interactive
Lecture
Provider:
CK-12 Foundation
Provider Set:
CK-12 Elementary Math
06/06/2019
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A web page and interactive applet show how to compute the perimeter of a polygon. A polygon is shown that can be resized by dragging its vertices. As you drag, the perimeter is continuously recalculated. Text on the page explains that the perimeter is the sum of the sides. For those who prefer it, in a formula that is given. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference interactive geometry reference book project at http://www.mathopenref.com.
Subject:
Geometry
Mathematics
Material Type:
Simulation
Provider:
Math Open Reference
Author:
John Page
05/07/2019
Unrestricted Use
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Definition of perimeter of polygon, list of items needed when calculating perimeter of polygon on coordinate plane; image of polygon on coordinate plane with additional information in hotspots. Detailed example of calculation of perimeter.
Subject:
Geometry
Mathematics
Material Type:
Interactive
Provider:
Michigan Virtual
07/19/2019
Rating
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An interactive applet and associated web page that show the relationship between the perimeter and area of a triangle. It shows that a triangle with a constant perimeter does NOT have a constant area. The applet has a triangle with one vertex draggable and a constant perimeter. As you drag the vertex, it is clear that the area varies, even though the perimeter is constant. Optionally, you can see the path traced by the dragged vertex and see that it forms an ellipse. A link takes you to a page where this effect is exploited to construct an ellipse with string and pins. The applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.
Subject:
Geometry
Mathematics
Material Type:
Simulation
Provider:
Math Open Reference
Author:
John Page
05/07/2019
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Students apply their understanding of perimeter while designing robots and finding their dimensions.
Subject:
Mathematics
Material Type:
Lesson Plan
Author:
Drew Polly
07/12/2020
Educational Use
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Students solidify their understanding of the terms "circumference" and "rotation" through the use of LEGO MINDSTORMS(TM) NXT robotics components. They measure the circumference of robot wheels to determine how far the robot can travel during one rotation of an NXT motor. They sharpen their metric system measurement skills by precisely recording the length of a wheel's circumference in centimeters, as well as fractions of centimeters. Through this activity, students practice brainstorming ways to solve a problem when presented with a given scenario, improve their ability to measure and record lengths to different degrees of precision, and become familiar with common geometric terms (such as perimeter and rotation).
Subject:
Applied Science
Engineering
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Ursula Koniges
09/18/2014
Educational Use
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Students learn how different characteristics of shapes—side lengths, perimeter and area—change when the shapes are scaled, either enlarged or reduced. Student pairs conduct a “scaling investigation” to measure and calculate shape dimensions (rectangle, quarter circle, triangle; lengths, perimeters, areas) from a bedroom floorplan provided at three scales. They analyze their data to notice the mathematical relationships that hold true during the scaling process. They see how this can be useful in real-world situations like when engineers design wearable or implantable biosensors. This prepares students for the associated activity in which they use this knowledge to help them reduce or enlarge their drawings as part of the process of designing their own wearables products. Pre/post-activity quizzes, a worksheet and wrap-up concepts handout are provided.
Subject:
Applied Science
Engineering
Material Type:
Lesson
Provider:
TeachEngineering
Author:
Denise W. Carlson
Evelynne Pyne
Lauchlin Blue
05/09/2019
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This short video and interactive assessment activity is designed to teach third graders an overview of area and perimeter.
Subject:
Mathematics
Material Type:
Assessment
Interactive
Lecture
Provider:
CK-12 Foundation
Provider Set:
CK-12 Elementary Math
06/06/2019
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This lesson is from Tools for NC Teachers. In this lesson, students consider the relationship between area and perimeter by trying to decide whether a shape can have a perimeter and area that are numerically the same.
Subject:
Mathematics
Material Type:
Activity/Lab
Lesson Plan
07/13/2019
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This is Tools for NC Teachers. In this lesson, students develop a deeper understanding of perimeter by solving and discussing perimeter problems involving rectangles with missing sides.
Subject:
Mathematics
Material Type:
Activity/Lab
Lesson Plan
07/13/2019
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This lesson is from Tools for NC Teachers. In this lesson, students develop a deeper understanding of perimeter by solving and discussing perimeter problems involving rectangles with missing sides. This is remixable.
Subject:
Mathematics
Material Type:
Activity/Lab
Lesson Plan
07/13/2019
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This lesson is from Tools for NC Teachers. In this lesson, students will design a dog pen using grid paper and square tiles to develop concepts about fixed perimeter and varying areas. This is remixable.
Subject:
Mathematics
Material Type:
Activity/Lab
Lesson Plan
07/12/2019
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This lesson is from Tools for NC Teachers. Students complete a series of activities related to area and perimeter. It can be used at the start of Clusters 2 or 4. This is remixable.
Subject:
Mathematics
Material Type:
Activity/Lab
Lesson Plan
07/12/2019
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This lesson is from Tools for NC Teachers. In this lesson, students explore the possible dimensions and areas of rectangles given a fixed perimeter. This is remixable.
Subject:
Mathematics
Material Type:
Activity/Lab
Lesson Plan | 2,572 | 12,024 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.09375 | 4 | CC-MAIN-2024-18 | latest | en | 0.885351 |
https://mapleprimes.com/questions/148643-How-To-Joinassign-A-set-Of-Values | 1,721,576,800,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763517747.98/warc/CC-MAIN-20240721152016-20240721182016-00258.warc.gz | 333,779,731 | 24,266 | # Question:how to join/assign a "set of values" to a "set of indices "
## Question:how to join/assign a "set of values" to a "set of indices "
Maple
i confused for finding a very special command that can join a "set of values" to a "set of indices " ?
also i can't use the map command for this ( guide ? )
like this :
{(1,1),(1,2),(2,1),(2,2)}
{1,2,3,4}
i want to join the two sets to form a complet set of equations index :
{(1,1)=1,(1,2)=2,(2,1)=3,(2,2)=4}
since this is just a simple example , but i need an efficent way for doing it in large size data (image processing)
`` ,-. . , . ( ` | | ,- | `-. |-. ,-. | , ,-. | |- ,-. . ) | | |-' |< | | |- | |-' `-' ' ' `-' ' ` `-' | `-' `-' -'`` | 260 | 773 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2024-30 | latest | en | 0.80944 |
https://mathspace.co/textbooks/syllabuses/Syllabus-1000/topics/Topic-19901/subtopics/Subtopic-263736/?textbookIntroActiveTab=overview | 1,638,657,016,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964363125.46/warc/CC-MAIN-20211204215252-20211205005252-00294.warc.gz | 465,217,425 | 67,231 | # 3.05 Time zones and the date line
Lesson
### Time zones
The world is divided into many time zones that allow different places to set their own time. The time zones are based on geography but are mainly influenced by politics, so they can seem strange or misplaced. In order to keep track and compare the time in different places, each location is given a UTC offset (Coordinated Universal Time) which allows it to be compared to other places around the world. Greenwich, a city in England was chosen to be the timezone with UTC $+0$+0 because it lies at $0^\circ$0° longitude. For this reason UTC was previously called GMT (Greenwich Mean Time).
Time zones around the world with the UTC offset given below
In the image above the time zones are represented by coloured bars, with the UTC time given at the bottom of the bar. In general, countries to the east of the UTC $+0$+0 time zone are ahead in time compared to UTC $+0$+0 and will have a "$+$+" symbol before the number, for example, Sydney is in UTC$+10$+10 which is $10$10 hours ahead of UTC $+0$+0.
Countries to the west of the UTC $+0$+0 will have time zones that are behind and will have a "$-$", for example, Los Angeles is in UTC $-8$8, which is $8$8 hours behind UTC $+0$+0.
Some time zones are not a whole number of hours away from UTC. For example Adelaide uses UTC $+9:30$+9:30 (or UTC $+9.5$+9.5) representing the hours and minutes. These regions are striped in the image above.
We can also use tables that show the UTC time for countries.
City UTC
Vancouver $-8$8
New York $-5$5
Rome $+1$+1
Dubai $+4$+4
New Delhi $+5.5$+5.5 ($+5:30$+5:30)
Perth $+8$+8
Melbourne $+10$+10
The time zone can be read off the table for the corresponding city.
#### Worked examples
##### Example 1
From the image below, what is the UTC time zone Paris is in?
Think: We can look at the colour of the region the city is in, and find what UTC time it relates to.
Do: The city is in a yellow region, which corresponds to the nearest yellow band, which is highlighted below.
This corresponds to UTC $+1$+1. Paris will be $1$1 hour ahead of UTC $+0$+0.
##### Example 2
From the table provided what is the time in New York when it is $11:00$11:00pm in Dubai?
City UTC
Vancouver $-8$8
New York $-5$5
Rome $+1$+1
Dubai $+4$+4
Melbourne $+10$+10
Think: We can first find the time difference between the two cities and then use this to find whether New York is ahead or behind of Dubai and by how much.
Do: New York uses UTC $-5$5 and Dubai uses UTC $+4$+4. The difference in hours is $4-\left(-5\right)=9$4(5)=9 hours. From the offsets $-5$5 is smaller than $+4$+4 which means that New York is behind Dubai in time.
If the time is $11:00$11:00 pm in Dubai then it will be $9$9 hours earlier in New York, which is $2:00$2:00 pm.
Summary
The world is divided up into time zones which are labelled with a UTC offset. This specifies the number of hours behind or ahead that time zone is from UTC $+0$+0. We can use the numbers and sign of the UTC to find the time difference between two places.
#### Practice questions
##### Question 1
Consider the map and complete the following:
1. When it is $17$17$:$:$00$00 in Cape Town what is the time in San Francisco?
$19$19$:$:$00$00
A
$1$1$:$:$00$00
B
$7$7$:$:$00$00
C
$3$3$:$:$00$00
D
$9$9$:$:$00$00
E
$15$15$:$:$00$00
F
$19$19$:$:$00$00
A
$1$1$:$:$00$00
B
$7$7$:$:$00$00
C
$3$3$:$:$00$00
D
$9$9$:$:$00$00
E
$15$15$:$:$00$00
F
##### Question 2
Consider the table of time zone information provided.
City UTC
Tijuana $-8$8
Mexico City $-6$6
Havana $-5$5
Kiev $+2$+2
Sri Lanka $+5.5$+5.5
Singapore $+8$+8
Seoul $+9$+9
1. When it is $9$9$:$:$00$00 am in Mexico City what is the time in Sri Lanka?
$2$2$:$:$30$30 am
A
$8$8$:$:$30$30 am
B
$8$8$:$:$30$30 pm
C
$3$3$:$:$00$00 am
D
$3$3$:$:$00$00 pm
E
$2$2$:$:$30$30 pm
F
$2$2$:$:$30$30 am
A
$8$8$:$:$30$30 am
B
$8$8$:$:$30$30 pm
C
$3$3$:$:$00$00 am
D
$3$3$:$:$00$00 pm
E
$2$2$:$:$30$30 pm
F
### The International Date Line
The International Date Line is the line that separates the two hemispheres on one side of the Earth at $180^\circ$180° longitude. It has an odd shape as it tries to avoid cutting through countries.
The International Date Line
#### Worked Example
##### EXAMPLE 3
What is the time and day in UTC $+12$+12 when it is $2:00$2:00 pm on Sunday in UTC $-11$11?
Think: We can calculate the time difference in the same way as normal. We take the difference of the two time zones.
The UTC $+12$+12 is ahead of UTC $-11$11, and there is a difference of $12-\left(-11\right)=23$12(11)=23 hours. is $23$23 hours ahead of. The time will be $1:00$1:00 pm, but on the Monday.
Reflect: When comparing time zones across the International Date Line, the change in time will be big enough that the day will normally change as well. Remember that it is always the countries with the positive UTC offset (like UTC $+12$+12) that will be ahead of the negative ones.
### Time zones in Australia
Australia has several time zones. It is also a country that uses Daylight Saving Time in the summer months. From the first Sunday of October to the first Sunday of April, some of the Australian states and territories turn their clocks forward one hour. This happens at $2$2 am on the first Sunday of October and finishes on the first Sunday of April, turning an hour back at $2$2 am. Below is the map of Australia outside of DST and during DST. Notice that New South Wales (NSW), Victoria (VIC), South Australia (SA), the Australian Capital Territory (ACT) and Tasmania (TAS) all use DST time and the other states and territories do not.
Summary
Some Australian states and territories observe Daylight Saving Time (DST) in the summer months, turning their clocks forward one hour. The states that observe DST are New South Wales (NSW), Victoria (VIC), South Australia (SA), the Australian Capital Territory (ACT) and Tasmania (TAS).
#### Practice question
##### Question 3
When the time is $14$14$:$:$15$15 in Perth what is the time in:
1. Sydney during No DST?
$11$11$:$:$15$15
A
$12$12$:$:$15$15
B
$16$16$:$:$15$15
C
$17$17$:$:$15$15
D
$11$11$:$:$15$15
A
$12$12$:$:$15$15
B
$16$16$:$:$15$15
C
$17$17$:$:$15$15
D
2. Sydney during DST?
$11$11$:$:$15$15
A
$12$12$:$:$15$15
B
$16$16$:$:$15$15
C
$17$17$:$:$15$15
D
$11$11$:$:$15$15
A
$12$12$:$:$15$15
B
$16$16$:$:$15$15
C
$17$17$:$:$15$15
D
### Outcomes
#### MA4-7NA
operates with ratios and rates, and explores their graphical representation | 2,086 | 6,535 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.75 | 4 | CC-MAIN-2021-49 | latest | en | 0.909414 |
https://metanumbers.com/140642 | 1,721,732,477,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763518029.87/warc/CC-MAIN-20240723102757-20240723132757-00522.warc.gz | 339,331,295 | 7,422 | 140642 (number)
140642 is an even six-digits composite number following 140641 and preceding 140643. In scientific notation, it is written as 1.40642 × 105. The sum of its digits is 17. It has a total of 2 prime factors and 4 positive divisors. There are 70,320 positive integers (up to 140642) that are relatively prime to 140642.
Basic properties
• Is Prime? no
• Number parity even
• Number length 6
• Sum of Digits 17
• Digital Root 8
Name
Name one hundred forty thousand six hundred forty-two
Notation
Scientific notation 1.40642 × 105 140.642 × 103
Prime Factorization of 140642
Prime Factorization 2 × 70321
Composite number
Distinct Factors Total Factors Radical ω 2 Total number of distinct prime factors Ω 2 Total number of prime factors rad 140642 Product of the distinct prime numbers λ 1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ 1 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0
The prime factorization of 140642 is 2 × 70321. Since it has a total of 2 prime factors, 140642 is a composite number.
Divisors of 140642
4 divisors
Even divisors 2 2 2 0
Total Divisors Sum of Divisors Aliquot Sum τ 4 Total number of the positive divisors of n σ 210966 Sum of all the positive divisors of n s 70324 Sum of the proper positive divisors of n A 52741.5 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G 375.023 Returns the nth root of the product of n divisors H 2.66663 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors
The number 140642 can be divided by 4 positive divisors (out of which 2 are even, and 2 are odd). The sum of these divisors (counting 140642) is 210966, the average is 52741.5.
Other Arithmetic Functions (n = 140642)
1 φ(n) n
Euler Totient Carmichael Lambda Prime Pi φ 70320 Total number of positive integers not greater than n that are coprime to n λ 70320 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π ≈ 13025 Total number of primes less than or equal to n r2 8 The number of ways n can be represented as the sum of 2 squares
There are 70,320 positive integers (less than 140642) that are coprime with 140642. And there are approximately 13,025 prime numbers less than or equal to 140642.
Divisibility of 140642
m n mod m
2 0
3 2
4 2
5 2
6 2
7 5
8 2
9 8
The number 140642 is divisible by 2.
• Semiprime
• Deficient
• Polite
• Square Free
Base conversion 140642
Base System Value
2 Binary 100010010101100010
3 Ternary 21010220222
4 Quaternary 202111202
5 Quinary 14000032
6 Senary 3003042
8 Octal 422542
10 Decimal 140642
12 Duodecimal 69482
20 Vigesimal hbc2
36 Base36 30iq
Basic calculations (n = 140642)
Multiplication
n×y
n×2 281284 421926 562568 703210
Division
n÷y
n÷2 70321 46880.7 35160.5 28128.4
Exponentiation
ny
n2 19780172164 2781922973489288 391255210837480442896 55026915362604924449779232
Nth Root
y√n
2√n 375.023 52.0042 19.3655 10.7059
140642 as geometric shapes
Circle
Diameter 281284 883680 6.21412e+10
Sphere
Volume 1.16529e+16 2.48565e+11 883680
Square
Length = n
Perimeter 562568 1.97802e+10 198898
Cube
Length = n
Surface area 1.18681e+11 2.78192e+15 243599
Equilateral Triangle
Length = n
Perimeter 421926 8.56507e+09 121800
Triangular Pyramid
Length = n
Surface area 3.42603e+10 3.27853e+14 114834
Cryptographic Hash Functions
md5 309ac58bcb2057f29f10ad161593de32 de9472290f85ce47f54c01f5d6e9c32b8b69724d f2825f4cc7a62823843aec05b617fc8bf56c303151d667680c8e18bb568300b5 95f76a404281044244f58d7d5f109729a841f378351177b12293be68289d43abf278ba64e0dccd870b8d2ab6328f8a55a8f568d47d81892b21b2a685dbcfbb53 e0de695bfcab6af00c96aafd790f863c8683a032 | 1,331 | 3,894 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.625 | 4 | CC-MAIN-2024-30 | latest | en | 0.827851 |
https://beyerhunde.de/2020/10/25/bsv-devcon-china-simplified-payment-verification-insight-and-emphasis-on-its-overlooked-features/ | 1,627,241,356,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046151760.94/warc/CC-MAIN-20210725174608-20210725204608-00632.warc.gz | 158,361,052 | 14,636 | # BSV Devcon China: Simplified Payment Verification – Insight and Emphasis on its Overlooked Features
Transaction data, the second part of data required for simplified verification First, let’s find out what transaction data is TxID is a hash value of transaction data Here are the Locktime, the Outpoint, and the Unlocking script, which is also known as input script, the Sequence number, and the Locking script, which is also known as output script If you know better names in Chinese to match these names, please let me know Next, we will discuss the third part of data required for SPV, that is Merkle Proof Let’s assume we are interested in this transaction This green dot represents the TxID of this transaction Our aim is to calculate the Merkle root Therefore, we need to know the hash value next to the TxID Once we know the value, we can link them together, and calculate the hash value for the upper layer Likewise, we need to know the hash value of the counterpart on the left hand side, so as to calculate the hash value for the upper layer Lastly, when we know the hash value of the counterpart on the right, we can then calculate the hash value of Merkle root at the very top After we have calculated the Merkle root, we need to compare it with the Merkle root in the block diagram, to see whether they are equal If they are equal, we can say that this transaction is already recorded on the blockchain So what is Merkle Proof exactly? Let’s take a look The transaction’s Merkle Proof is made up of 4 parts The first part is the TxID of the transaction The second part is the hash value of its counterpart in the transaction The third part is the hash value of its counterpart on the upper layer The fourth part is the hash value of its counterpart on the further upper layer A transaction’s Merkle Proof can be seen as the minimum information required to calculate the Merkle root of the Merkle tree, where the transaction is located Let me repeat it A transaction’s Merkle Proof can be seen as the minimum information required to calculate the root of the Merkle tree, where the transaction is located Okay, now we have gone through the three parts of data required for the existence of simplified verification They are the block headers list, the transaction data and the transaction’s Merkle Proof, respectively Next, we will see how simplified verification is applied in a payment scenario First, we have a five-starred seller, Ruby, who sells commodities online She wants to complete online payments by means of SPV First, she needs to get connected with a Bitcoin network and obtain the block headers list via the Bitcoin network, because the block headers list is one of the three parts of data required for SPV She can collect the first part of data through this connecting with the Bitcoin network This part of data needs to be updated in real-time On the other hand, we have a gamer, Ming When shopping online, he comes across a game console presented by our five-starred seller Ruby, falls for it right away and so he decides to buy it Ming initiates a payment transaction to Ruby If you are familiar with BIP270, you will notice that this BIP applies perfectly in this case Ruby may first send a request for payment to Ming, which is a template of payment transaction After completing it, Ming can send the payment transaction back to Ruby, who then successfully collects the second part of data required for simplified verification, that is, the transaction data Finally, Ruby needs one more thing, the Merkle Proof, to start the SPV Ruby sends the payment transaction to the Bitcoin network and then waits patiently Once the payment transaction is recorded in a certain block, Ruby will receive a Merkle Proof from the Bitcoin network, | 764 | 3,766 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2021-31 | latest | en | 0.925536 |
https://nl.mathworks.com/matlabcentral/profile/authors/5971188 | 1,652,818,210,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662520817.27/warc/CC-MAIN-20220517194243-20220517224243-00157.warc.gz | 492,670,114 | 20,473 | Community Profile
# Viswanath Hariharan
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# On rare occasions, frost has been occuring as far south as
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On rare occasions, frost has been occuring as far south as Miami, but there is not record of a frost in Key West.
A) -
B) frost has occured as far south as Miami, but no records exist
C) as far south as Miami, frost has occured, but no records exist
D) places as far south as Miami have had unusual occurances of frost, but no record exists
E) frost has occured as far south as Miami, but no record has been
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22 Jan 2006, 01:07
(B) stands tall and proud.
Using a little CR logic-
1. present perfect indicates that in the event of another meteorological anomaly, frost may reoccur in Miami.
2. "records" needs to be plural to substatiate the claim. IE: compared from a variety of weather sources.
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22 Jan 2006, 01:19
GMATT73 wrote:
(B) stands tall and proud.
Using a little CR logic-
1. present perfect indicates that in the event of another meteorological anomaly, frost may reoccur in Miami.
2. "records" needs to be plural to substatiate the claim. IE: compared from a variety of weather sources.
Agree with Matt. IMO, present perfect tense is better coz present continuous perfect tense is used to describe sth happening non-stop. Here we have "on rare occasions" ----> not continuous ---> present perfect tense is much better.
My money on B.
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22 Jan 2006, 01:40
Agree with Matt & Laxie, B it is!
BTW, Laxie, its so nice to see you back!
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22 Jan 2006, 02:03
TeHCM wrote:
Agree with Matt & Laxie, B it is!
BTW, Laxie, its so nice to see you back!
hik, i'm still here ...it's just that i have no internet access at home so i seem reclusive . How have you been, buddy?!!
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22 Jan 2006, 13:09
I'm doing great! It was hard getting back on the saddle but I'm riding again!
I missed seeing you, Duttsit, Christoph, HIMALAYA, gamjatang's posts!!!!
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22 Jan 2006, 15:57
B - it is .. for me
A- "frost has been occuring" - implies that there is frost occurring even now. This contradicts with opening modifying statement : On rare occasions - which btw, implies of a past event
B-
C - modifier problem ... "On rare occasions" cannot be modifying "as far south..."
D -too wordy ..
E - if you insert the choice you can see it just does not read right
".... but no record has been of a frost in Key West..."
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22 Jan 2006, 18:35
Go with B. However first I thought D should be OK, but "On rare occasions" and "unusual occurances" together would be redundant.
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24 Jan 2006, 13:30
The OA is B. I was totally ready to go with it, when I thought shouldnt the sentence say frost occured in places as far south as Miami, rather than saying frost occured as far south as Miami? Thus I chose D, even though it looked too wordy as suggested by Bhai and 5elements.
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24 Jan 2006, 13:32
Although one more reason to reject D seems to be its usage of record rather than records.
24 Jan 2006, 13:32
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Problem with Sprite
Marcin Piwko Member #15,823 December 2014 In my program there is an icon of player and icon of enemy. Player can move using ALLEGRO_KEY_RIGHT, ALLEGRO_KEY_DOWN,ALLEGRO_KEY_RIGHT, ALLEGRO_KEY_LEFT. To create AI I used srand(time(NULL)); function, then: #SelectExpand 1if (events.timer.source == enemy1TypeTimer) 2{ 3 enemy.choDir = rand() % 3; 4} program generates 3 random numbers: 0,1 and 2. If 1- the following direction will be chosen : Right or Left, if 2- Top or Bottom.I create another condition to chose between right and left, top or bottom: #SelectExpand 2if (enemy.choDir == 1){ 3 if (enemy.y 4#include 5#include 6#include 7#include 8using namespace std; 9 10int ScreenWidth = 800, ScreenHeight = 600; 11bool done = false; 12 13enum Direction{ DOWN, LEFT, RIGHT, UP }; 14 15struct Player 16{ 17 float x = 10; 18 float y = 10; 19 float moveSpeed = 5; 20 21 bool draw = true; 22 bool active = false; 23 24 int dir = DOWN; 25 int sourceX=32; 26 int sourceY=0; 27}; 28struct Enemy{ 29 float x = 10; 30 float y = 10; 31 float moveSpeed = 5; 32 33 bool draw = true; 34 bool active = false; 35 36 int dir = DOWN; 37 int sourceX = 32; 38 int sourceY = 0; 39 40 int choDir= 0; //choose direction horizontal or upright 41}; 42 43void PlayerInitialConditions(Player& player,float StartXPosition,float StartYPostition, float StartMoveSpeed)//in next Updates add health, timer, bullets etc. 44{ 45 player.x = StartXPosition; 46 player.y = StartYPostition; 47 player.moveSpeed = StartMoveSpeed; 48} 49void EnemyInitialConditions(Enemy &enemy, float StartXPosition, float StartYPostition, float StartMoveSpeed) 50{ 51 enemy.x = StartXPosition; 52 enemy.y = StartYPostition; 53 enemy.moveSpeed = StartMoveSpeed; 54} 55 56void InitialConditions(Player& player, Enemy &enemy) 57{ 58 PlayerInitialConditions(player, 10, 10, 5); 59 EnemyInitialConditions(enemy, 200, 200, 3); 60} 61 62int main(){ 63 64 const float FPS = 60; 65 const float frameFPS = 15;//1) 66 67 if (!al_init()) 68 { 69 al_show_native_message_box(NULL, "ERROR", NULL, "Could not initialize Allegro 5", NULL, NULL); 70 return -1; 71 } 72 73 al_set_new_display_flags(ALLEGRO_WINDOWED); 74 ALLEGRO_DISPLAY *display = al_create_display(ScreenWidth, ScreenHeight);//creating window with dimensions: 800:600 px 75 al_set_window_position(display, 200, 200);//place from left top positioning the frame of display 76 al_set_window_title(display, "Marcin Piwko RLZ"); 77 78 if (!display)//show this message if sth wrong with display 79 { 80 al_show_native_message_box(display, "Sample Title", "Display Settings", "Display window was not created succesfully", NULL, ALLEGRO_MESSAGEBOX_ERROR); 81 return -1; 82 } 83 84 al_install_keyboard(); 85 al_init_image_addon(); 86 ALLEGRO_BITMAP *playerBMP = al_load_bitmap("PlayerImage1.png"); 87 ALLEGRO_BITMAP *enemy1TypeBMP = al_load_bitmap("enemy1.png"); 88 89 90 ALLEGRO_KEYBOARD_STATE keyState;//pokazuje jaki klawisz został aktualnie wciśniety 91 92 ALLEGRO_TIMER *timer = al_create_timer(3.0 / FPS);//predkosc ruchu gracza 93 ALLEGRO_TIMER *frameTimer = al_create_timer(0.5 / frameFPS);//2) 94 ALLEGRO_TIMER *enemy1TypeTimer = al_create_timer(5.0 / FPS); 95 96 97 ALLEGRO_EVENT_QUEUE *event_queue = al_create_event_queue(); 98 al_register_event_source(event_queue, al_get_timer_event_source(timer)); 99 al_register_event_source(event_queue, al_get_timer_event_source(frameTimer)); 100 al_register_event_source(event_queue, al_get_timer_event_source(enemy1TypeTimer)); 101 102 al_register_event_source(event_queue, al_get_display_event_source(display)); 103 al_register_event_source(event_queue, al_get_keyboard_event_source()); 104 105 Player player; 106 Enemy enemy; 107 108 InitialConditions(player, enemy); 109 110 srand(time(NULL)); 111 al_start_timer(timer); 112 al_start_timer(frameTimer); 113 al_start_timer(enemy1TypeTimer); 114 115 while (!done) 116 { 117 ALLEGRO_EVENT events; 118 al_wait_for_event(event_queue, &events); 119 al_get_keyboard_state(&keyState); 120 if (events.type == ALLEGRO_EVENT_DISPLAY_CLOSE) 121 { 122 done = true; 123 } 124 125 //Implementation of AI 126 if (events.timer.source == enemy1TypeTimer) 127 { 128 enemy.choDir = rand() % 3; 129 } 130 131 else if (events.type == ALLEGRO_EVENT_TIMER) 132 { 133 if (events.timer.source == timer)//5 134 { 135 player.active = true; 136 if (al_key_down(&keyState, ALLEGRO_KEY_DOWN)) 137 { 138 player.y += player.moveSpeed; 139 player.dir = DOWN; 140 } 141 else if (al_key_down(&keyState, ALLEGRO_KEY_UP)) 142 { 143 player.y -= player.moveSpeed; 144 player.dir = UP; 145 } 146 else if (al_key_down(&keyState, ALLEGRO_KEY_RIGHT)) 147 { 148 player.x += player.moveSpeed; 149 player.dir = RIGHT; 150 } 151 else if (al_key_down(&keyState, ALLEGRO_KEY_LEFT)) 152 { 153 player.x -= player.moveSpeed; 154 player.dir = LEFT; 155 } 156 else 157 player.active = false; 158 159 //Artificial inteligence used: 160 enemy.active = true; 161 if (enemy.choDir == 1){ 162 if (enemy.y= al_get_bitmap_width(playerBMP)) 201 player.sourceX = 0; 202 203 player.sourceY = player.dir; 204 } 205 player.draw = true; 206 207 208 209 if (events.timer.source = frameTimer)//6) 210 { 211 if (enemy.active== true) 212 enemy.sourceX += al_get_bitmap_width(enemy1TypeBMP) / 3; 213 else 214 enemy.sourceX = 32; 215 216 if (enemy.sourceX >= al_get_bitmap_width(enemy1TypeBMP)) 217 enemy.sourceX = 0; 218 219 enemy.sourceY = enemy.dir; 220 } 221 enemy.draw = true; 222 223 224 } 225 226 227 228 229 230 231 if (player.draw||enemy.draw){ 232 al_draw_bitmap_region(playerBMP, player.sourceX, player.sourceY * al_get_bitmap_height(playerBMP) / 4, 32, 32, 233 player.x, player.y, NULL); 234 al_draw_bitmap_region(enemy1TypeBMP, enemy.sourceX, enemy.sourceY * al_get_bitmap_height(enemy1TypeBMP) / 4, 32, 32, 235 enemy.x, enemy.y, NULL); 236 al_flip_display(); 237 al_clear_to_color(al_map_rgb(0, 0, 0)); 238 } 239 } 240 241 al_destroy_display(display); 242 al_destroy_timer(timer); 243 al_destroy_bitmap(playerBMP); 244 al_destroy_bitmap(enemy1TypeBMP); 245 al_destroy_event_queue(event_queue); 246 return 0; 247}
Trent Gamblin Member #261 April 2000 You need to use "else if" here:``` else if (enemy.choDir == 2) ``` Otherwise anytime choDir is 1, the else following this gets executed, setting the enemy to inactive.
Gideon Weems Member #3,925 October 2003 Trent's right. Also, you've got a couple assignments in your if statements:if (events.timer.source = frameTimer)//6)In addition, this block seems to be redundant.That's a cool, little sprite you've got there.
Marcin Piwko Member #15,823 December 2014 I can't believe that the answer is so simple! Thx you both!!! It works!!
Go to: Allegro Development Installation, Setup & Configuration Allegro.cc Comments Off-Topic Ordeals The Depot Game Design & Concepts Programming Questions Recent Threads | 2,041 | 6,920 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2018-34 | longest | en | 0.559353 |
http://www.thecodingforums.com/threads/yet-another-rounding-issue.861795/ | 1,477,279,593,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988719465.22/warc/CC-MAIN-20161020183839-00550-ip-10-171-6-4.ec2.internal.warc.gz | 722,679,720 | 12,468 | # Yet another rounding issue
Discussion in 'Ruby' started by Manu Sankala, Feb 21, 2010.
1. ### Manu SankalaGuest
At school I was taught that five is always rounded up. Later on I've
been told that sometimes five is rounded to closest even number. Neither
of these seem to be the case with ruby:
irb(main):044:0> RUBY_VERSION
=> "1.8.7"
irb(main):045:0> (217.5).round
=> 218
irb(main):046:0> (218.5).round
=> 219
irb(main):047:0> (2.175*100).round
=> 217
irb(main):048:0> (2.185*100).round
=> 219
irb(main):049:0> sprintf('%.2f',2.175)
=> "2.17"
irb(main):050:0> (2.175*100.0).round/100.0
=> 2.17
Can someone please tell me how do I round 2.175 to 2.18, besides
((2.175*100).to_s+'9').to_f.round/100.0 ?
-
Manu S
--
Posted via http://www.ruby-forum.com/.
Manu Sankala, Feb 21, 2010
2. ### Jean-Julien FleckGuest
Hello,
> Can someone please tell me how do I round 2.175 to 2.18, besides
> ((2.175*100).to_s+'9').to_f.round/100.0 ?
I guess bigdecimal should be the answer
>> (2.175*100).round
=3D> 217
>> require 'bigdecimal'
=3D> true
>> a =3D BigDecimal("2.175")
=3D> #<BigDecimal:1014bd230,'0.2175E1',8(8)>
>> (a*100).round.to_s
=3D> "0.218E3"
Cheers,
--=20
JJ Fleck
PCSI1 Lyc=E9e Kl=E9ber
Jean-Julien Fleck, Feb 21, 2010
3. ### Mohit SindhwaniGuest
On 22/2/2010 1:39 AM, Manu Sankala wrote:
> At school I was taught that five is always rounded up. Later on I've
> been told that sometimes five is rounded to closest even number. Neither
> of these seem to be the case with ruby:
>
> irb(main):044:0> RUBY_VERSION
> => "1.8.7"
> irb(main):045:0> (217.5).round
> => 218
> irb(main):046:0> (218.5).round
> => 219
> irb(main):047:0> (2.175*100).round
> => 217
> irb(main):048:0> (2.185*100).round
> => 219
> irb(main):049:0> sprintf('%.2f',2.175)
> => "2.17"
> irb(main):050:0> (2.175*100.0).round/100.0
> => 2.17
>
> Can someone please tell me how do I round 2.175 to 2.18, besides
> ((2.175*100).to_s+'9').to_f.round/100.0 ?
>
Actually, this is because of the way floating point variables are
handled in a computer.
You could try:
a = 2.175
b = a + 0.0005
c = ((b * 100).round) / 100.0
irb(main):010:0> a = 2.175
=> 2.175
irb(main):011:0> b = a + 0.0005
=> 2.1755
irb(main):012:0> c = (b * 100).round / 100.0
=> 2.18
irb(main):013:0> a = 2.185
=> 2.185
irb(main):014:0> b = a + 0.0005
=> 2.1855
irb(main):015:0> c = (b * 100).round / 100.0
=> 2.19
Cheers,
Mohit.
22/2/2010 | 1:46 AM.
Mohit Sindhwani, Feb 21, 2010
4. ### Manu SankalaGuest
Mohit Sindhwani wrote:
> You could try:
> a = 2.175
> b = a + 0.0005
> c = ((b * 100).round) / 100.0
Well this is basically same as my
((some_float_here*100).to_s+'9').to_f.round/100.0
except that in my version I don't need to know how many decimals the
float originally has. "b = a + 0.0005" would fail if 'a' has mode than 3
decimals.
Since
((float_here*100).to_s+'9').to_f.round/100.0
and
(BigDecimal(float_here.to_s)*100).round.to_s.to_f/100
seem to be about as fast I think I'll go with bigfloat as it seems less
like a hack. | 1,210 | 2,997 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2016-44 | latest | en | 0.767853 |
https://de.zxc.wiki/wiki/Ganzrationale_Funktion | 1,656,404,792,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103360935.27/warc/CC-MAIN-20220628081102-20220628111102-00724.warc.gz | 248,856,443 | 31,631 | # Quite rational function
The articles polynomial and fully rational function overlap thematically. Help me to better differentiate or merge the articles (→ instructions ) . To do this, take part in the relevant redundancy discussion . Please remove this module only after the redundancy has been completely processed and do not forget to include the relevant entry on the redundancy discussion page{{ Done | 1 = ~~~~}}to mark. Menner ( discussion ) 10:59, Dec. 2, 2017 (CET)
Graph of a fully rational function of the 5th degree
Polynomial of degree 0, ${\ displaystyle f (x) = 2}$
Polynomial of degree 1, ${\ displaystyle f (x) = 2-x / 2}$
Polynomial of degree 2, ${\ displaystyle f (x) = x ^ {2} -x-2}$
Polynomial of degree 3, ${\ displaystyle f (x) = {\ tfrac {(x + 4) (x + 1) (x-2)} {4}}}$
Polynomial of degree 4, ${\ displaystyle f (x) = {\ tfrac {(x + 4) (x + 1) (x-1) (x-3)} {14}} + 0 {,} 5}$
A completely rational function or polynomial function is a function in mathematics that can be described as the sum of power functions with natural exponents . This means that such functions can only be described using the addition, subtraction and multiplication operations. Wholly rational functions belong to the rational functions and in turn contain the linear and quadratic functions as special cases .
This article deals mainly with the completely rational functions over the real numbers, which are common in school mathematics. Further information on possible generalizations of the concept can be found in the article Polynomial .
## definition
A completely rational function is a real function that is expressed in the shape
${\ displaystyle f (x) = a_ {n} x ^ {n} + a_ {n-1} x ^ {n-1} + \ dotsb + a_ {2} x ^ {2} + a_ {1} x + a_ {0} = \ sum _ {k = 0} ^ {n} a_ {k} x ^ {k}}$
can be written, where a natural number and real numbers are and applies. The number is called the degree of the function, the numbers are its coefficients . The coefficient is called the lead coefficient. The summand is called the absolute term, the summands and are sometimes referred to as the linear or quadratic term. ${\ displaystyle n \ in \ mathbb {N}}$${\ displaystyle a_ {n}, a_ {n-1}, \ ldots, a_ {2}, a_ {1}, a_ {0}}$ ${\ displaystyle a_ {n} \ neq 0}$${\ displaystyle n}$${\ displaystyle a_ {n}, a_ {n-1}, \ ldots, a_ {2}, a_ {1}, a_ {0}}$${\ displaystyle a_ {n}}$${\ displaystyle a_ {0}}$${\ displaystyle a_ {1} x}$${\ displaystyle a_ {2} x ^ {2}}$
The representation of the completely rational function given here is its normal form . For example, a completely rational function can also be represented by means of linear factors or by means of the Horner schemes .
## Examples
• The function with the term is a completely rational function of degree 3 with the coefficients and .${\ displaystyle f (x) = - 2x ^ {3} + 3x ^ {2} -5x + 4}$${\ displaystyle -2,3, -5}$${\ displaystyle 4}$
• With the function , the function term must first be rewritten into a sum by opening the brackets:${\ displaystyle f \ colon x \ mapsto -2x (x-1) (x + 3) ^ {2}}$
{\ displaystyle {\ begin {aligned} f (x) & = - 2x (x-1) (x + 3) ^ {2} = (- 2x ^ {2} + 2x) (x ^ {2} + 6x +9) \\ & = - 2x ^ {4} -10x ^ {3} -6x ^ {2} + 18x, \ end {aligned}}}
so the degree is 4 and the coefficients are and .${\ displaystyle -2, -10, -6,18}$${\ displaystyle 0}$
• For an entirely rational function of degree with the coefficients , the function term can be written as .${\ displaystyle 5}$${\ displaystyle -1.0, {\ sqrt {2}}, - 2 \ pi, 0.1}$${\ displaystyle f (x) = - x ^ {5} + {\ sqrt {2}} x ^ {3} -2 \ pi x ^ {2} +1}$
## Special cases
• There are constant functions for${\ displaystyle n = 0}$ ${\ displaystyle f \ colon x \ mapsto a_ {0}}$
• There are linear functions for (instead of writing for the slope here , and instead of writing for the -axis section ).${\ displaystyle n = 1}$ ${\ displaystyle f \ colon x \ mapsto a_ {1} x + a_ {0}}$${\ displaystyle m}$${\ displaystyle a_ {1}}$${\ displaystyle n}$${\ displaystyle y}$${\ displaystyle a_ {0}}$
• For there are quadratic functions (instead of and one writes here , and ).${\ displaystyle n = 2}$ ${\ displaystyle f \ colon x \ mapsto a_ {2} x ^ {2} + a_ {1} x + a_ {0}}$${\ displaystyle a, b}$${\ displaystyle c}$${\ displaystyle a_ {2}}$${\ displaystyle a_ {1}}$${\ displaystyle a_ {0}}$
• There are cubic functions for .${\ displaystyle n = 3}$ ${\ displaystyle f \ colon x \ mapsto a_ {3} x ^ {3} + a_ {2} x ^ {2} + a_ {1} x + a_ {0}}$
• For sometimes called quartic functions .${\ displaystyle n = 4}$
• If only and all other coefficients are equal , then a power function with a natural exponent results .${\ displaystyle a_ {n} \ neq 0}$${\ displaystyle 0}$ ${\ displaystyle f \ colon x \ mapsto a_ {n} x ^ {n}}$
## Algebraic properties
The addition and multiplication of two completely rational functions result in completely rational functions. Thus the set of completely rational functions forms an algebra${\ displaystyle \ mathbb {R}}$ . For the degree of completely rational functions and the estimation or equality apply ${\ displaystyle f}$${\ displaystyle g}$
${\ displaystyle \ deg (f + g) \ leq \ max (\ deg f, \ deg g)}$
and
${\ displaystyle \ deg (f \ cdot g) = \ deg f + \ deg g}$.
Denotes the degree of . ${\ displaystyle \ deg f}$${\ displaystyle f}$
In addition, the concatenation of two completely rational functions is again a completely rational function, that is, a completely rational function is obtained again if a completely rational function is used for the function variable.
## symmetry
• If all exponents are even numbers, then the graph of the function is axisymmetric to the y-axis. The function is then also called straight ; it applies .${\ displaystyle f (-x) = f (x)}$
• If all exponents are odd numbers, the graph of the function is point-symmetric to the origin. The function is then also called odd ; it applies .${\ displaystyle f (-x) = - f (x)}$
• If both even and odd exponents occur, the graph does not have a simple symmetry; but it can still be symmetrical to other axes or points.
Examples:
• The graph of the function is symmetrical about the -axis (only even exponents: 6, 4 and 2).${\ displaystyle f \ colon x \ mapsto -2x ^ {6} + 3x ^ {4} -x ^ {2}}$${\ displaystyle y}$
• The graph of the function is symmetrical to the origin (only odd exponents: 7 and 1).${\ displaystyle f \ colon x \ mapsto x ^ {7} + x}$
• The graph of the function has no simple symmetry (odd and even exponents: 3 and 0), but is point-symmetric about its inflection point .${\ displaystyle f \ colon x \ mapsto x ^ {3} +1}$${\ displaystyle W (0 | 1)}$
• The graph of every rational function of the second degree is axisymmetric to the vertical axis through its vertex .
• The graph of every fully rational function of the third degree is point-symmetric to its inflection point .
## Boundary behavior
In general, the behavior for is determined by the summands with the highest exponent, the behavior for by the summands with the lowest exponents. ${\ displaystyle x \ to \ pm \ infty}$${\ displaystyle x \ to 0}$
### growth
Wholly rational functions can be understood as linear combinations of powers . Therefore they grow more slowly (for sufficiently large values) than any exponential function whose base is greater than 1, regardless of the coefficients.
### Behavior for very large and very small x values
All completely rational functions diverge for . The exact behavior depends on whether the degree n is even or odd and the sign of the leading coefficient ; the graph behaves exactly like the graph of a power function with the term . In the following, the resulting set of values is also given for the case that the definition set is. ${\ displaystyle x \ to \ pm \ infty}$${\ displaystyle a_ {n}}$${\ displaystyle g (x) = a_ {n} x ^ {n}}$ ${\ displaystyle \ mathbb {W}}$ ${\ displaystyle \ mathbb {D} = \ mathbb {R}}$
n straight n odd
${\ displaystyle a_ {n}> 0}$ The graph runs from top left to top right, so: for is bounded downwards (by the absolute minimum of the function)
${\ displaystyle f (x) \ to \ infty}$${\ displaystyle x \ to \ pm \ infty}$
${\ displaystyle \ mathbb {W}}$
The graph runs from bottom left to top right, so: for and for
${\ displaystyle f (x) \ to - \ infty}$${\ displaystyle x \ to - \ infty}$${\ displaystyle f (x) \ to \ infty}$${\ displaystyle x \ to \ infty}$
${\ displaystyle \ mathbb {W} = \ mathbb {R}}$
${\ displaystyle a_ {n} <0}$ The graph runs from bottom left to bottom right, so: for is bounded upwards (by the absolute maximum of the function)
${\ displaystyle f (x) \ to - \ infty}$${\ displaystyle x \ to \ pm \ infty}$
${\ displaystyle \ mathbb {W}}$
The graph runs from top left to bottom right, so: for and for
${\ displaystyle f (x) \ to \ infty}$${\ displaystyle x \ to - \ infty}$${\ displaystyle f (x) \ to - \ infty}$${\ displaystyle x \ to \ infty}$
${\ displaystyle \ mathbb {W} = \ mathbb {R}}$
### Behavior for x values close to zero
All completely rational functions are finite. More precisely, the following applies: the graph intersects the -axis , the slope at this point is given by. The tangent at the point of intersection with the axis therefore always has the equation${\ displaystyle x \ to 0}$${\ displaystyle y}$${\ displaystyle a_ {0}}$${\ displaystyle a_ {1}}$${\ displaystyle y}$${\ displaystyle y = a_ {1} x + a_ {0}}$
### example
The graph of the function runs like the graph of the function , i.e. from top left to bottom right (degrees odd, leading coefficient ). The following applies to the function values: for and for . For , on the other hand, it runs like the graph of , i.e. it intersects the -axis and has the slope there . ${\ displaystyle f \ colon x \ mapsto -2x ^ {5} + 4x ^ {3} -3x + 1}$${\ displaystyle x \ to \ pm \ infty}$${\ displaystyle g \ colon x \ mapsto -2x ^ {5}}$${\ displaystyle n = 5}$${\ displaystyle a_ {5} = - 2 <0}$${\ displaystyle f (x) \ to \ infty}$${\ displaystyle x \ to - \ infty}$${\ displaystyle f (x) \ to - \ infty}$${\ displaystyle x \ to \ infty}$${\ displaystyle x \ to 0}$${\ displaystyle h (x) = - 3x + 1}$${\ displaystyle y}$${\ displaystyle 1}$${\ displaystyle -3}$
## zeropoint
### Linear factorization
If the function term of a completely rational function is given as a product of linear factors (some of which can also occur multiple times) and possibly a completely rational function g without zeros, i.e.
${\ displaystyle f (x) = (x-x_ {1}) ^ {k_ {1}} \ cdot (x-x_ {2}) ^ {k_ {2}} \ dotsm (x-x_ {m}) ^ {k_ {m}} \ cdot g (x),}$
so are the zeros. The natural numbers are called the multiples of the zeros . ${\ displaystyle x_ {1}, x_ {2}, \ dotsc, x_ {m}}$ ${\ displaystyle k_ {1}, k_ {2}, \ dotsc, k_ {m}}$
Example: The function
${\ displaystyle f \ colon x \ mapsto -0 {,} 01 \ cdot x ^ {3} \ cdot (x-2) \ cdot (x + 3) ^ {2} \ cdot (x ^ {2} +1 )}$
has the triple zero , the single zero and the double / double zero ; the factors and , on the other hand, cannot become zero for none , so do not provide any further zeros. ${\ displaystyle x_ {1} = 0}$${\ displaystyle x_ {2} = 2}$${\ displaystyle x_ {3} = - 3}$${\ displaystyle -0 {,} 01}$${\ displaystyle x ^ {2} +1}$${\ displaystyle x}$
The linear factorization of a completely rational function can be determined, for example, with the help of the polynomial division . From the fundamental theorem of algebra it follows that every completely rational function over the complex numbers can be broken down into a product of linear factors. If the function only has real coefficients, it follows that with every complex zero, the conjugate complex number is also a zero. This means that every completely rational function over the real numbers can be represented uniquely (except for the sequence) as a product of linear and quadratic terms.
The multiplicity of zeros is also directly related to the derivatives of the function: is a -fold zero of if and only if and . ${\ displaystyle x_ {0}}$${\ displaystyle k}$${\ displaystyle f}$${\ displaystyle f (x_ {0}) = f '(x_ {0}) = \ dotsb = f ^ {(k-1)} (x_ {0}) = 0}$${\ displaystyle f ^ {(k)} (x_ {0}) \ neq 0}$
### Course of the graph at the zeros
• The graph intersects the axis at every zero point of odd multiplicity . The function values change their sign there. In the case of simple zeros, the axis is cut at an angle greater than 0 °. For every zero point of odd multiplicity greater than or equal to three, the slope at the zero point is 0; the function graph has a terrace point .${\ displaystyle x}$${\ displaystyle x}$
• The graph touches the -axis at every zero point of even multiple . The function values do not change their sign there. At every such zero the function graph has an extreme point .${\ displaystyle x}$
graphic illustration:
simple zero three, five, 2k + 1 zero position double, quadruple, 2k zero position
If you also consider the behavior for , the following graph results for the above example : ${\ displaystyle x \ to \ pm \ infty}$${\ displaystyle f (x) = - 0 {,} 01x ^ {3} (x-2) (x + 3) ^ {2} (x ^ {2} +1)}$
### Methods for calculating the zeros
To find zeros, the algebraic equation has to be solved. There are (among others) the following methods for this: ${\ displaystyle f (x) = 0}$
• Linear equations can be solved directly using equivalent transformations . The zeros are then always easy.
• For quadratic equations , there are various methods of solution; see the corresponding article. The following applies: if there are two different solutions, both are simple; if there is only one solution, it is double.
• Often times, the function term can be factored directly by factoring out powers of or by using the binomial formulas . The multiplicities can then be read off directly in the linear factor decomposition.${\ displaystyle x}$
• If only and are not equal to zero, i.e. for functions with terms of the form , the zeros result simply with the help of the -th root . These zeros are then always easy.${\ displaystyle a_ {n}}$${\ displaystyle a_ {0}}$${\ displaystyle f (x) = a_ {n} x ^ {n} + a_ {0}}$${\ displaystyle n}$
• The substitution method helps with some equations, especially biquadratic ones . The following applies: If you have a (positive!) Single or double solution of the corresponding quadratic equation after the substitution, this results in two single or double zeros of the function itself.
• If a zero can be found by trial and error, the associated linear factor can be divided out with the help of a polynomial division and an algebraic equation of a lower degree is obtained. The multiplicities of the zeros are obtained here simply by counting how often a zero comes out in the calculation. The following sentences are helpful for finding a zero by trying it out:
• If all coefficients are integer , then all integer zeros are dividers of the absolute term (note: there may also be non-integer zeros). If the coefficients are all rational numbers , you can always achieve by multiplying by the main denominator that all the coefficients are integers.${\ displaystyle a_ {0}}$
• If all the coefficients have the same sign, the zeros cannot be positive.
• The Cardan formulas can be used for fully rational third-degree functions ; for fully rational functions of the fourth degree there are similar formulas for quartic equations .
• Zero points can also be determined approximately, for example with the Newton method .
### number
With the help of the polynomial division one can show that a completely rational function of degree can have zeros at most (multiples counted). ${\ displaystyle n}$${\ displaystyle n}$
If one also considers the behavior of the graph for , the behavior at the zeros ( change of sign ) and the continuity , it also follows: if the degree is even or odd, then the total number of zeros (including multiples) is even or odd . In particular, it follows: Every completely rational function of odd degree has at least one zero. ${\ displaystyle x \ to \ pm \ infty}$
There are also other, more advanced rules for the number of zeros such as Descartes' sign rule and the Sturm chain .
## Differentiation and integrability
### Derivative function
Completely rational functions can be differentiated over completely continuously . Functions that can be differentiated completely or completely are called whole functions . The derivative function can be determined using the factor , sum and power rule . This gives for the function with the rule ${\ displaystyle \ mathbb {R}}$ ${\ displaystyle \ mathbb {R}}$${\ displaystyle \ mathbb {R}}$
${\ displaystyle f (x) = \ sum _ {k = 0} ^ {n} a_ {k} x ^ {k}}$
the derivative function
${\ displaystyle f '(x) = \ sum _ {k = 1} ^ {n} ka_ {k} x ^ {k-1}}$.
### Integrability and antiderivative
Every completely rational function can be integrated on a compact interval . In addition, every completely rational function has an antiderivative . This can be specified explicitly with the usual integral rules. The following applies:
${\ displaystyle \ int {\ bigg (} \ sum _ {k = 0} ^ {n} a_ {k} x ^ {k} {\ bigg)} dx = \ sum _ {k = 0} ^ {n} \ int a_ {k} x ^ {k} dx = \ sum _ {k = 0} ^ {n} {\ frac {a_ {k}} {k + 1}} x ^ {k + 1} + c, }$
where is any constant. ${\ displaystyle c \ in \ mathbb {R}}$
### Examples
For the function with the term
${\ displaystyle f (x) = 2x ^ {3} -4x ^ {2} + 5x-1}$
the derivative function results with the term
{\ displaystyle {\ begin {aligned} f '(x) & = (2x ^ {3} -4x ^ {2} + 5x-1)' \\ & = (2x ^ {3}) '- (4x ^ {2}) '+ (5x)' - 1 '\\ & = 2 (x ^ {3})' - 4 (x ^ {2}) '+ 5 (x ^ {1})' - 1 (x ^ {0}) '\\ & = 2 \ cdot 3x ^ {2} -4 \ cdot 2x + 5 \ cdot 1x ^ {0} -1 \ cdot 0 \\ & = 6x ^ {2} -8x + 5 \ end {aligned}}}
In this case one obtains for the antiderivatives
${\ displaystyle \ int (2x ^ {3} -4x ^ {2} + 5x-1) dx = {\ frac {1} {2}} x ^ {4} - {\ frac {4} {3}} x ^ {3} + {\ frac {5} {2}} x ^ {2} -x + c, c \ in \ mathbb {R}.}$
## Extreme points
To determine the extreme points, the points with a horizontal tangent, i.e. the zeros of the first derivative, must first be calculated. The first derivation is again a completely rational function, but of degree ; The same methods can therefore be used as for calculating the zero. ${\ displaystyle n-1}$
### General rules
• If the function itself has a zero of even multiplicity, then its graph has an extreme point there (see above under zeros).
• If the sign of the first derivative changes from - to + at one point, there is a minimal point there; if it changes from + to -, there is a maximum place; if the sign does not change, there is no extreme point there (but a terrace point ).
• If the second derivative is positive or negative at a zero of the first derivative, the first derivative there changes its sign from - to + (minimum digit) or from + to - (maximum digit). If the second derivative is equal to zero, there can still be an extreme point at this point, but there can also be a terrace point there. Means other than the second derivative are then necessary to differentiate.
• If a zero of the first derivative has an odd multiplicity, the function itself has an extreme there; if, on the other hand, it has a multiplicity, the function has a terrace point at this point .
### number
From the theorem about the number of zeros of a completely rational function it follows that a completely rational function of degree can have at most extreme points. ${\ displaystyle n}$${\ displaystyle n-1}$
If one also considers the behavior of the graph for and the behavior at the zeros (change of sign), it also follows: if the degree is even or odd, then the total number of extreme positions is odd or even. ${\ displaystyle x \ to \ pm \ infty}$
In particular, it follows: Every completely rational function of an even degree has an absolute minimum or maximum (depending on whether the leading coefficient is positive or negative). ${\ displaystyle a_ {n}}$
## Turning points
(see also the section on turning points in the article curve discussion )
To determine the turning points, the zeros of the second derivative, the so-called flat points, must first be calculated. The second derivation is again a completely rational function, but of degree ; The same methods can therefore be used as for calculating the zero. ${\ displaystyle n-2}$
### General rules
• If the function itself has a zero point of odd multiplicity greater than or equal to three, then its graph has a terrace point there , i.e. also a turning point (see above for zeros).
• If the sign of the second derivative changes at one point, there is a turning point there.
• If the third derivative is not equal to zero at a zero of the second derivative, the sign of the second derivative changes there (turning point). If the third derivative is zero, there can still be a turning point at this point, but it does not have to. Means other than the third derivative are then necessary to differentiate.
• If a zero of the second derivative has an even multiplicity, the function itself has no turning point there; on the other hand, if the zero of the first derivative has an odd multiplicity, the function itself has a turning point there. If the first derivative is also zero at this point, the graph of the function has a terrace point there .
• The following applies particularly to functions of the third degree:
• The high and low point (if any) are always symmetrical to the point of inflection (this follows because the graphs of functions of the third degree are always symmetrical to their point of inflection, see above).
• If the function itself has three (not necessarily different) real zeros, the turning point results as its mean value, weighted with the multiples. (If, on the other hand, there is only one real zero, the complex zeros must also be taken into account when calculating the mean value .)
### number
From the theorem about the number of zeros of a completely rational function it follows that a completely rational function of degree can have at most turning points. ${\ displaystyle n}$${\ displaystyle n-2}$
If one also considers the behavior of the graph for and the behavior at the zeros (change of sign), it also follows: if the degree is even or odd, the total number of turning points is even or odd. ${\ displaystyle x \ to \ pm \ infty}$
In particular, it follows: Every completely rational function of an odd degree greater than or equal to three has at least one turning point.
## Establishing functional terms
Often a problem has to be solved as follows: There are some points and possibly additional conditions (such as gradients in these points), and a completely rational function is sought whose graph runs through these points and possibly fulfills the additional conditions. In order to find this completely rational function, one first sets up the function term in the most general possible form (the degree is either given directly or must be determined from the other given information), forms any necessary derivatives of the function in this general form and then sets the given conditions. This leads to a linear system of equations for the coefficients of the function; instead of , etc. these are usually referred to here with etc. By solving this system of equations, one then obtains the term of the function sought. ${\ displaystyle a_ {n}}$${\ displaystyle a_ {n-1}}$${\ displaystyle a, b}$
Example: We are looking for a completely rational function of the lowest possible degree, whose graph is symmetrical to the axis and has a slope of 2 at the point of inflection . ${\ displaystyle y}$${\ displaystyle W (1 | 3)}$
• Since the graph should be symmetrical about the -axis, the degree must be even and the function term can only contain even exponents.${\ displaystyle y}$
• Since there is supposed to be a turning point, the degree cannot be 2 (a function of the second degree has no turning point); so the lowest possible grade is 4.
• The functional term in its most general form is:
${\ displaystyle f (x) = ax ^ {4} + bx ^ {2} + c}$
• Since we are talking about a turning point, two derivatives are required:
${\ displaystyle f '(x) = 4ax ^ {3} + 2bx}$
${\ displaystyle f '' (x) = 12ax ^ {2} + 2b}$
• The graph runs through the point , so the following applies ( insert - and coordinate in )${\ displaystyle W}$${\ displaystyle x}$${\ displaystyle y}$${\ displaystyle f}$
${\ displaystyle 3 = a \ times 1 ^ {4} + b \ times 1 ^ {2} + c}$
• The graph has slope 2 there, so the following applies ( insert coordinate and slope in )${\ displaystyle x}$${\ displaystyle f '}$
${\ displaystyle 2 = 4a \ cdot 1 ^ {3} + 2b \ cdot 1}$
• The point is a turning point, so the following applies ( must be 0 at the turning point )${\ displaystyle W}$${\ displaystyle f ''}$
${\ displaystyle 0 = 12a \ cdot 1 ^ {2} + 2b}$
• Overall, the linear system of equations results
${\ displaystyle a + b + c = 3}$
${\ displaystyle 4a + 2b = 2}$
${\ displaystyle 12a + 2b = 0}$
• Solving this system of equations gives . So the term of the function we are looking for is:${\ displaystyle a = -0 {,} 25; \; b = 1 {,} 5; \; c = 1 {,} 75}$
${\ displaystyle f (x) = - 0 {,} 25x ^ {4} +1 {,} 5x ^ {2} +1 {,} 75}$
## Application examples
• Many of the curves that occur in nature and technology can be described relatively well using completely rational functions, for example terrain formations, ski jumps or the deflection of beams.
• Quite rational functions often appear in geometric applications. Examples:
• If you cut out squares of the side length at the corners of a rectangular cardboard (length , width ) and then fold the cardboard into a box that is open at the top, the volume of the box is the same .${\ displaystyle l}$${\ displaystyle b}$${\ displaystyle x}$${\ displaystyle V (x) = 4x ^ {3} -2 (l + b) x ^ {2} + lbx}$
• If you stack balls (e.g. oranges in the supermarket) to form a three-sided pyramid, with balls lying along a base edge, then the pyramid contains balls as a whole .${\ displaystyle n}$${\ displaystyle {\ tfrac {1} {6}} (n ^ {3} + 3n ^ {2} + 2n)}$
• Tax tariffs are often described by completely rational functions ( PDF ).
• In economic applications, the revenue function is often an entirely rational function of the third degree.
• Since completely rational functions are particularly simple, more complicated functions are often approximated by completely rational ones (cf. Taylor series and Weierstrass's approximation theorem ). This approach is used in particular in analysis and numerics . Alternatively, there are also situations in which a finite number of function values are specified and a function is sought that runs through these points. These can polynomial interpolation can be used. In addition, a finite set of function values can also be interpolated piece-wise using completely rational functions. This procedure is called spline interpolation . If you want to evaluate a completely rational function at one point numerically efficiently (optimized for computers), the Horner scheme can be used.
## literature
• H. Schneider, G. Stein: Mathematics 11 and Mathematics 12: Analysis for non-technical training courses in the technical college.
• R. Schöwe, J. Knapp, R. Borgmann: Analysis: Commercial-economic direction for technical college. | 7,289 | 27,324 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 186, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.4375 | 4 | CC-MAIN-2022-27 | longest | en | 0.890955 |
http://blog.softinway.com/en/7-1-multi-criterion-optimization-of-hpc-of-powerful-steam-turbines-at-nominal-operational-mode/ | 1,576,200,279,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575540547536.49/warc/CC-MAIN-20191212232450-20191213020450-00410.warc.gz | 23,137,410 | 17,017 | #### 7.1 Multi-Criterion Optimization of HPC of Powerful Steam Turbines at Nominal Operational Mode
##### Chapter 7 Introduction: Experience and Examples of Optimization of Axial Turbines Flow Paths
In this chapter, as an example of practical use of the developed theory of optimal design of axial turbines flow paths, the results of the studies, related to the optimization of parameters of flow path of the high pressure cylinders (HPC) of 220, 330 and 540 MW capacities turbines, operating at nominal mode, as well as examples of optimization turbo-expander and low pressure turbine of gas turbine unit, taking into account the mode of its operation, are presented. The entire complex of calculation research was conducted using mathematical models of flow path (FP) of axial turbines, described in Chapter 2.
In addition, in the studies variants of mathematical models of FP “with the specified profiles” [38] were also used, which allowed with more accuracy determine geometric characteristics of turbine cascades, in particular, the inlet geometric angles of working and nozzle cascades, that are changing with the changing of stagger angles of the profiles. The latter had a significant impact on the amount of additional losses related to the incidence angle of inlet flow of working fluid.
##### 7.1.1 A Preliminary Study of Influence of Quality Criteria Weights Coefficients on the Optimization Results
Practice of the optimal design of axial turbines cylinders has showed that when optimizing steam turbine cylinder with extraction of working fluid for regeneration and heat supplying at least two criteria – the efficiency of the cylinder flow path and its capacity must be taking into account [38, 40-42].
Using the convolution of quality criteria in accordance with (1.37) allows efficiently solve the multi-criterion optimization problems corresponding the Pareto front.
As an example of the effectiveness of the use of convolution (1.37) the results of the optimization of HPC FP of a powerful steam turbine by two criteria – power and cylinder efficiency for different values of the weight coefficients μi are presented in Table 7.1 and Fig. 7.1.
Numbers on the curve corresponds to the numbers of optimization problem in the Table 7.1.
##### 7.1.2 Optimization of HPC Parameters of the 220 MW Capacity Turbine for Nuclear Power Plant
The number of optimization parameters – 33:
• – level 1 (cylinder) – optimized for 19 parameters:
• – Root diameter and height of the nozzle blades of the first stage of the cylinder.
• – Meridional disclosing of the channels of the nozzle and working cascades.
• – Effective exit angles of the nozzle and working cascades of all turbine stages.
• 2-nd level (stage) – optimized for 14 parameters:
• – The number of the blades in the nozzle cascades for all turbine stages.
• – The number of the blades in the working cascades for all turbine stages.
Quality criteria applied when optimizing – the criterion vector that includes the normalized values of internal relative efficiency of the cylinder ηoi and its power (N) with equal weight coefficients.
The results of the optimization of the HPC FP of the 220 Mw capacity turbine [39] are listed in Table 7.2 and in Fig. 7.2, where ηd – Moliere diagram efficiency of FP η’ – the ratio of efficiency of the stages to Moliere diagram efficiency of the initial variant of the cylinder ηoi – internal efficiency of FP; Δηd – gain of the internal efficiency of the optimal FP; N – power; ΔN – the power gain of the optimal variant of the HPC FP.
Improvement of the quality indicators of the optimized FP obtained through:
• – rational distribution of the cylinder heat drop, having in its disposal, between the stages;
• – some decreasing of the axial speed components and ensuring closer to axial outlet working fluid from the stages, resulting in reducing the exit velocity losses;
• – reducing the incidence angles, that provides the improving efficiency of the nozzle and working cascades;
• – increasing the mean diameter of the stages, that led to obtaining the optimal values of the ratio of the velocities u/C0
• – reducing the specific weight of the losses near the hub and the shroud boundaries by increasing the height of the blades;
• – the optimal value of the nozzle and working cascades relative pitch, which also led to an increase of their effectiveness.
The final variant is obtained by optimization taking into account the technological restrictions on the production of the flow path parts. This explains the slight decreasing of efficiency and cylinder capacity compared to the best option without restrictions.
The optimal variant of HPC FP of the 220 MW capacity turbine for nuclear power plant is obtained, which characterized by high perfection levels of aerodynamic indices, providing a boost of power on 5.4 MW, of internal efficiency on 2.71% and Moliere diagram efficiency on 2.27% as compared to the initial version of FP.
##### 7.1.3 Optimization of High-Pressure Cylinder Parameters of the 330 MW Capacity Turbine
The number of optimization parameters – 55:
• – level 1 (cylinder)-optimized for 44 parameters:
• – Root diameter and height of the nozzle blades of the first stage of the cylinder.
• – Meridional disclosing of the channels of the nozzle and working cascades.
• – Effective exit angles of the nozzle and working cascades of all turbine stages.
• – 2-nd level (stage)-optimized for 11 parameters:
• – The number of the blades in the working cascades for all turbine stages.
Quality criteria applied when optimizing – the criterion vector that includes the normalized values of Moliere diagram efficiency of the cylinder (ηd) and its power (N) with equal weight coefficients.
The results of the optimization of the HPC FP of the turbine 330 MW capacity turbine are listed in Table 7.3 and in Fig. 7.3, where ηd – Moliere diagram efficiency of FP; η’ – the ratio of efficiency of the stages to Moliere diagram efficiency of the initial variant of the cylinder; ηoi – internal efficiency of FP;Δηoi – gain of the internal efficiency of the optimal FP; N – power; ΔN – the power gain of the optimal variant of the HPC FP.
Improvement of the quality indicators of the optimized FP obtained through:
• – more rational distribution of the cylinder heat drop, having in its disposal, between the stages;
• – application of the optimal configuration of meridional shape of FP with a slightly reduced heights blades;
• – increasing value of the effective nozzle exit angles, providing the reduction of the incidence angles on the working cascades;
• – improving the efficiency of working cascades through the optimal choice of stagger angles and numbers of the blades, resulting in a significant reduction of losses from the incidence angle;
• – reducing the degree of reaction level of the stages and, as a consequence, reducing the losses from root and radial leakages.
Practical application of the developed optimization theory provided the solution of the task: the optimum variant HPC PF of the 330 MW capacity turbine was obtained, which characterized by high perfection levels of aerodynamic indices, providing a boost of power on 6.2 MW, of the relative internal efficiency on 5.76% and Moliere diagram efficiency on 3.94% in comparison with the initial version of FP.
##### 7.1.4 Optimization of the HPC Flow Path Parameters of the 540 MW Capacity Turbine
Features of the initial variant of the HPC FP:
• – FP of the 9 stages HPC has high enough quality integral indicators, which have been achieved thanks to the very high level of aerodynamic perfection of the flow path of the cylinder:
• – numbers of the nozzle and working cascades blades are close to the optimal values;
• – the inlet flow incidence angles at the nozzle and work cascades are close enough to the possible minimum values given used profiles and blades production technology;
• – the root degrees of reaction provide fairly low levels of hub leakages;
• – the use of highly effective radial seals has significantly reduced radial leakages.
However, in the construction of FP reserves of possible efficiency gains were identified associated with not quite rationally distribution of disposable heat drop between the cylinder stages and somewhat inflated level of root leakages in first stage.
The number of optimization parameters of HPC FP of the turbine 540 MW capacity – 55:
• – level 1 (cylinder) – optimized for 37 parameters:
• – Root diameter and height of the nozzle blades of the first stage of the cylinder.
• – Meridional disclosing of the channels of the nozzle and working cascades.
• – Effective exit angles of the nozzle and working cascades of all turbine stages.
Due to the fact that in the initial variant of the HPC FP number of the nozzle and working cascades blades near by the optimal values, the second level of optimization (stage) was not used in this task.
Quality criteria applied when optimizing – the criterion vector that includes the normalized values of Moliere diagram efficiency of the cylinder (ηd) and its power (N) with equal weight coefficients. The results of the optimization of the HPC FP of the turbine 540 MW capacity are listed in Fig. 7.4, where (N) – power and η’ – the ratio of efficiency of the stages to Moliere diagram efficiency of the initial variant of the cylinder.
Improvement of the quality indicators of the optimized FP obtained through:
• – a more rational distribution of the disposal cylinder heat drop, between the stages, thereby improving the integral indicators of the cylinder quality;
• – some decrease of axial velocity component and ensuring closer to axial outlet of working fluid from the stages, that reduced the exit velocity losses, improving inlet conditions for nozzles cascades (which led to an improvement in their effectiveness);
• – close to optimal values of velocities ratio (u/C0), obtained by increasing the mean diameter of the stages;
• – reduction in the share of the losses near the hub and the shroud boundaries associated with increasing the heights of the blades;
• – using in 6–9 stages of the blades a highly effective 1MMC profile (Chapter 5), which provided a good matching flow inlet angles and the geometric inlet angles of the working cascades, that resulted in increasing their efficiency;
• – obtaining the optimal twist laws of the β2e angles at the outlet of the working wheels of 6–9 stages that contributed to the rational distribution of the gas-dynamic parameters along the radius of these stages.
So, the practical application of the developed optimization theory secured the solution of the requested task: the optimum variant of HPC FP of the 540 MW capacity turbine was obtained, which characterized by high perfection levels of aerodynamic indices, providing a boost of power on 1.4 MW, of inner efficiency on 1.52% and Moliere diagram efficiency on 1.63% in comparison with the initial version of FP. | 2,280 | 10,960 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.625 | 3 | CC-MAIN-2019-51 | latest | en | 0.914116 |
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# P 1 V 1 = P 2 V 2
Boyle’s Law. y = A / x. Pressure = A Volume. PV = constant. P 1 V 1 = P 2 V 2. ↑ P ↓ V. Inverse relationship. ↓P ↑V. Practice Problem A gas occupies a volume of 3.86 L at 0.750 atm . At what pressure will the volume be 4.86 L ?. V 1. P 1. ? P 2. V 2.
## P 1 V 1 = P 2 V 2
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### Presentation Transcript
1. Boyle’s Law y = A / x Pressure = A Volume PV = constant P1V1 = P2V2 ↑P ↓V Inverse relationship ↓P ↑V
2. Practice Problem A gas occupies a volume of 3.86 L at 0.750 atm. At what pressure will the volume be 4.86 L? V1 P1 ? P2 V2 P1V1 = P2V2 (0.750 atm)(3.86 L) = P2(4.86 L) (0.750 atm)(3.86 L) = P2 (4.86 L) = 0.596 atm
3. Charles’Law V= constant T y = mx + b V1=V2 T1 T2 K = 0C + 273 Direct relationship ↑T ↑V -273
4. Practice Problem A 4.50 L container of nitrogen gas at 28.0 0C is heated to 56.0 0C. Assuming the volume of the container can vary, what is the new volume of the gas? T1 V1 T2 ? V2 V1=V2 T1 T2 4.50 L=V2 301 K 329 K K = 0C + 273 V2 = 4.92 L
5. Gay-Lussac’s Law y = mx + b P= constant T P1= P2 T1 T2 K = 0C + 273 Direct relationship -273 0C ↑T ↑P
6. Practice Problem A gas cylinder contains 40.0 L of gas at 45.0 0C and has a pressure of 650. torr. What will the pressure be if the temperature is changed to 100. 0C? T1 ? P2 P1 T2 P1= P2 T1 T2 650. torr = P2 318 K 373 K K = 0C + 273 P2 = 762 torr
7. P, V PV = constant Combined Gas Law P, T P = constant T PV = constant T V, T V = constant T P1V1 = P2V2 T1 T2 K = 0C + 273 STP = Standard Temperature & Pressure 00C, 273 K 1 atm
8. Practice Problem 15.00 L of gas at 45.0 0C and 800. torr is heated to 400.0C, and the pressure changed to 300. torr. What is the new volume? V1 T1 P1 P2 T2 ? V2 P1V1 = P2V2 T1 T2 K = 0C + 273 (800. torr)(15.00 L) = (300. torr) V2 318 K 673 K V2 = 84.7 L
9. Practice Problem To what temperature must 5.00 L of oxygen at 50. 0C and 600. torr be heated in order to have a volume of 10.0 L and a pressure of 800. torr? ? T2 V1 T1 P1 V2 P2 P1V1 = P2V2 T1 T2 K = 0C + 273 (600. torr)(5.00 L) = (800. torr)(10.0 L) 323 K T2 T2 = 861 K = 588 0C
10. Do problems: 1 & 2 pg 443 4-6 pg 446 8 & 9 pg 448 11& 12 pg 450
More Related | 920 | 2,166 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.09375 | 4 | CC-MAIN-2024-26 | latest | en | 0.769744 |
https://www.physicsforums.com/threads/backround-independence-and-the-definition-of-distance.507576/ | 1,547,973,274,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547583705091.62/warc/CC-MAIN-20190120082608-20190120104608-00487.warc.gz | 888,022,326 | 18,054 | # Backround independence and the definition of distance
1. Jun 17, 2011
### jfy4
Hi everyone,
General relativity gives us the definition of the distance between two "events"
$$d=\int \sqrt{g_{\alpha\beta}dx^\alpha dx^\beta}.$$
I don't think this will complicate things but lets say its between two balls. Now like I said, with GR we have the definition of the distance between these two balls, which is possible through the gravitational field $g_{\alpha\beta}$. However, as far as I know the gravitational field does not prescribe the distance between the gravitational field and the balls. This troubles me since, the gravitational field is clearly a quantity that depends on what's close by, so to speak. However, there should not be a background distance to "tell" the gravitational field what it is "close" to.
In summary, while the gravitational field provides a metric for the distance between balls, it does not provide a metric, for the metric and the balls. How does the gravitational field "know" where the balls are?
Thank you,
2. Jun 17, 2011
### Passionflower
Do not mistake the spacetime distance between two events with the spatial distance between two objects.
An analogy (not exact but it may help you see the situation) about background independence:
Imagine the distance between two boats on a lake without any wind, one places a very light string over the flat surface of the water between the ships and and reads the length of the string to determine the distance. Now imagine the water having waves, you cannot really take this string over the waves between the boats because the waves are constantly moving and changing and the boats are as well.
3. Jun 17, 2011
### jfy4
My mistake, but to make my point in your language, how does the water know how close it is to the boats?
4. Jun 17, 2011
### Passionflower
It does not know how close the boats are, all that is happens is to 'know' what is immediately surrounding for gravity to work, we could integrate all those surroundings in stationary spacetimes to get some sense of distance between the boats but in non stationary spacetimes we can not.
In the case of two balls the spacetime is not stationary, in some solutions with two balls we even have gravitational waves interact at infinity and then 'coming back' in the solution.
5. Jun 17, 2011
### PAllen
I'll just add a little to what Passionflower said (which I agree with).
First, even mathematically, you integral is over some specified path. To describe a length along this particular spacetime path, the path must be spacelike. While in SR, there is unique geodesic which can unambiguously be called the distance, in GR, unless the points are close together, there will be multiple geodesics. Thus 'distance' rather than proper length of a path, is ill defined in GR. Further, a physically meaningful distance would have to be described in relation to some measuring method and apparatus, which would impose some definition of simultaneity, and that would specify the path you should integrate.
Ok, so that is just about distance between events in spacetime whose geometry is determined by the mass/energy around. If you are talking about 'balls', they are going to have timelike paths through spacetime. If small and not subject to any forces, these will be timelike geodesics. If they are not small, the Einstein field equations would need to be solved for the whole system including them (producing gravitational waves, and generally requiring numeric or perturbative methods of solution). It is the field equations that describe how each influences the geometry and responds (with finite propagation time) to the changing geometry produced by motion of other bodies. The whole point of field theory is that nothing know how far away something is. Each object produces influences with finite propagation speed and responds to local influences propagating from other objects, all in a complex, non-linear way (in general).
6. Jun 17, 2011
### pervect
Staff Emeritus
I'm not quite sure what your question is. Viewed as a geometric entity, the metric gives you the distances and the proper times between any two nearby points. You haven't talked at all about the tricky issue of splitting space time into a spatial part and a time part, the mere existence of a metric as a geometric entity won't necessarily perform that task for you. I'm not sure if it's useful to go into more on this point other than to point out it's something that needs to be accomplished, and that the metric of GR is a 4-dimensional entity, not a 3-dimensional one.
If you add to the metric Einstein's field equations (which you haven't mentioned at all yet), the metric also tells you the distribution of matter that is present - given enough mathematical sophistication and ability.
You'd need to take the metric, bang it around with some high-powered math, and get it to spit out the various tensors that describe its curvature. At the end, you'll come up with the Einstein tensor, which will be proportional to the matter density. The matter density won't be a single number, either, for reasons that are probably two complex to get into. But you will have, at the end, starting with the metric, using Einstein's equations, an expression for the matter density, even if it's more complex than what you're used to.
After you've done this, you can say "aha - this metric describes two balls, and their gravitational field". But it doesn't tell you really how to figure out what the metric you want is to get the two balls, it does tell you if you write down a metric if it describes two balls.
There's some more advanced stuff you can do - if you take the ADM route, you can specify some 3-d hypersurface at "some instant of time", with some three dimensional metric (which appears to be more in lines of your thinking, anyway, the GR metric includes space and time and you seem to be thinking only space). But you need something else, something that describes how the spatial surface is "curved" in its time embedding. (Technically it's K_ab, a rank two tensor, according to Wald). Given this data, you can in theory predict the global time evolution of the manifold, it's 3d metric, and the K_ab tensor field.
By "can do it" I mean that mathematicaly there is in theory a unique solution. Finding it numerically so that it makes physical sense and the errors stay within reasonable bounds is a job for a team of specialists with supercomputers.
Last edited: Jun 17, 2011
7. Jun 17, 2011
### jfy4
Thanks for the responses, I'm familiar with the curvature tensors etc... but that does not answer my question, probably since you couldn't tell what the question was. I'll try again, sorry for not being more clear. I'm going to do this completely by analogy with the hopes that this doesn't fail miserably.
If we consider and upside down canoe representing the curvature of spacetime, we assign a metric to the canoe. Now if we place two marbles on the canoe, yes they will start to move and the whole situation is full of math, but we can also put two tacks in and put a string between the tacks which gives the distance between these tacks. I hope we are ok so far.
My question is about that there is another distance here that we aren't considering, and that is the distance between the marbles and the canoe. I mean, we set them on there, but I mean in real-life, how do bodies know "where" they are relative to the gravitational field? Is there a mechanism responsible for a bodies relative location to the gravitational field?
8. Jun 17, 2011
### atyy
When we use the gravitational field as a spacetime metric, it is typically not background independent.
The reason is that we use test particles or ideal clocks to measure the proper time between two events. We assume that the test particles or ideal clocks do not contribute to spacetime curvature, and simply measure it. The background independence is due to spacetime curvature caused by all other mass-energy in the universe excluding our test particles and ideal clocks.
So in the canoe example, the most fundamental thing is we do not know what the "shape" of the canoe is until we put the balls in. However, we also do not have a meaning for "shape" until we can measure with string and tacks.
So more properly, the analogy is that we do not know what the "X-field" of the canoe is until we put the balls in. After the balls are put in, and we know the X-field, we interpret the X-field as "shape" by assuming that our string and tacks only measure the X-field without changing it. This latter assumption is wrong, since strings and tacks have mass-energy like balls and should also change the X-field. However, usually the change due to the strings and tacks is small enough to be ignored for practical purposes.
Last edited: Jun 17, 2011
9. Jun 17, 2011
### jfy4
Thanks, that's very enlightening. I'll think about that for a bit.
10. Jun 17, 2011
### Passionflower
We are OK in that the distance you mention is the spacetime distance between two events NOT locations.
Points in spacetime are events not locations!
The worldlines of the (free falling) bodies follow the local curvature.
11. Jun 17, 2011
### DrGreg
I don't understand what you are getting at here. Isn't it obvious that the distance between the marbles and the canoe is zero?
The "gravitational field" is everywhere, so the distance between any body and the "gravitational field" is zero.
12. Jun 17, 2011
### jfy4
Yes, this seems very much like the case, I'm not attempting to say I can't see that that isn't true, I'm wondering if there is a reason for this. Given that there is no background metric to discern this "distance" between the gravitational field and a body, how does a body know where it is relative to the gravitational field.
atyy response seems to suggest an answer, I'm mulling it over.
Thanks for the response. | 2,194 | 9,930 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5625 | 4 | CC-MAIN-2019-04 | latest | en | 0.954792 |
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### Samacheer Kalvi 10th Maths Solutions Chapter 1 Relations and Functions Ex 1.1
Tamilnadu State Board helps you to revise the complete Syllabus and score more marks in your examinations.
10th Maths Exercise 1.1 Samacheer Kalvi Question 1.
Find A × B, A × A and B × A
(i) A = {2,-2,3} and B = {1,-4}
(ii) A = B = {p,q]
(iii) A= {m,n} ; B = (Φ)
Solution:
(i) A = {2,-2,3}, B = {1,-4}
A × B = {(2, 1), (2, -4), (-2, 1), (-2, -4), (3,1) , (3,-4)}
A × A = {(2, 2), (2,-2), (2, 3), (-2, 2), (-2, -2), (-2, 3), (3, 2), (3, -2), (3,3) }
B × A = {(1, 2), (1, -2), (1, 3), (-4, 2), (-4, -2), (-4,3)}
(ii) A = B = {(p,q)]
A × B = {(p, p), {p, q), (q, p), (q, q)}
A × A = {(p, p), (p, q), (q, p), (q, q)}
B × A = {(p,p), {p, q), (q, p), (q, q)}
(iii) A = {m,n} × Φ
A × B = { }
A × A = {(m, m), (m, n), (n, m), (n, n)}
B × A = { }
10th Maths Exercise 1.1 Question 2.
Let A= {1,2,3} and B = {× | x is a prime number less than 10}. Find A × B and B × A.
A = {1,2,3}, B = {2, 3, 5, 7}
A × B = {1,2,3} × {2, 3, 5, 7}
= {(1, 2) (1, 3) (1, 5) (1, 7) (2, 2)
(2, 3) (2, 5) (2, 7)(3, 2) (3, 3) (3, 5) (3, 7)}
B × A = {2, 3, 5, 7} × {1,2,3}
= {(2, 1)(2, 2)(2, 3)(3, 1)(3, 2)(3, 3) (5, 1)(5, 2)(5, 3) (7, 1) (7,2)(7, 3)}
10th Maths Exercise 1.1 In Tamil Question 3.
If B × A = {(-2, 3),(-2, 4),(0, 3),(0, 4),(3, 3), (3, 4)} find A and B.
Solution:
B × A ={(-2, 3), (-2, 4), (0, 3), (0, 4), (3, 3), (3, 4)}
A = {3, 4), B = { -2, 0, 3}
Samacheer Kalvi 10th Maths Exercise 1.1 Question 4.
If A= {5, 6}, B = {4, 5 ,6}, C = {5, 6, 7}, Show that A × A = (B × B) ∩ (C × C)
A ={5,6}, B = {4,5,6}, C = {5, 6,7}
A × A = {5, 6} × {5,6}
= {(5, 5) (5, 6) (6, 5) (6, 6)} ….(1)
B × B = {4, 5, 6} × {4, 5, 6}
= {(4, 4)(4, 5)(4, 6)(5, 4)(5, 5) (5, 6) (6, 4)(6, 5) (6, 6)}
C × C = {5,6,7} × {5,6,7}
= {(5, 5)(5, 6)(5, 7)(6, 5)(6, 6) (6, 7)(7, 5)(7, 6) (7, 7)}
(B × B) ∩ (C × C) = {(5, 5)(5, 6)(6, 5)(6, 6)} ….(2)
From (1) and (2) we get
A × A = (B × B) ∩ (C × C)
Ex 1.1 Class 10 Samacheer Question 5.
Given A ={1, 2, 3}, B = {2, 3, 5}, C = {3, 4} and D = {1, 3, 5}, check if (A ∩ C) x (B ∩ D) = (A × B) ∩ (C × D) is true?
Solution:
LHS = {(A∩C) × (B∩D)
A ∩C = {3}
B ∩D = {3, 5}
(A ∩ C) × (B ∩ D) = {(3, 3) (3, 5)} ………….. (1)
RHS = (A × B) ∩ (C × D)
A × B = {(1, 2), (1, 3), (1, 5), (2, 2), (2, 3), (2, 5), (3, 2), (3, 3), (3, 5)}
C × D = {(3, 1), (3, 3), (3, 5), (4, 1), (4, 3), (4, 5)}
(A × B) ∩ (C × D) = {(3, 3), (3, 5)} …(2)
∴ (1) = (2) ∴ It is true.
10th Maths Book Exercise 1.1 Question 6.
Let A = {x ∈ W | x < 2},
B = {x ∈ N | 1 < 1 < × < 4} and
C = {3,5}. Verify that
(i) A × (B ∪ C) = (A × B) ∪ (A × C)
(ii) A × (B ∩ C) = (A × B) ∩ (A × C)
(iii) (A ∪ B) × C = (A × C) ∪ (B × C)
(i) A = {0, 1}
B = {2,3,4}
C = {3,5}
(i) A × (B ∪ C) = (A × B) ∪ (A × c)
B ∪ C = {2, 3,4} ∪ {3,5}
= {2, 3, 4, 5}
A × (B ∪ C) = {0, 1} × {2, 3, 4, 5}
= {(0, 2) (0, 3) (0, 4) (0, 5) (1, 2) (1, 3)(1, 4)(1, 5)} ….(1)
A × B = {0, 1} × {2,3,4}
= {(0,2) (0,3) (0,4) (1,2) (1,3) (1,4) }
A × C = {0, 1} × {3, 5}
{(0, 3) (0, 5) (1,3) (1,5)}
(A × B) ∪ (A × C) = {(0, 2) (0, 3) (0, 4) (0, 5) (1, 2)(1, 3)(1, 4)(1, 5)} ….(2)
From (1) and (2) we get
A × (B ∪ C) = (A × B) ∪ (A × C)
(ii) A × (B n C) = (A × B) n (A × C)
B ∩ C = {2,3,4} ∩ {3,5}
= {3}
A × (B ∩ C) = {0, 1} × {3}
= {(0,3) (1,3)} ….(1)
A × B = {0,1} × {2,3,4}
= {(0, 2) (0, 3) (0, 4) (1,2) (1,3) (1,4)}
A × C = {0,1} × {3,5}
{(0, 3) (0, 5) (1,3) (1,5)}
(A × B) n (A × C) = {(0, 3) (1, 3)} ….(2)
From (1) and (2) we get
A × ( B n C) = (A × B) n (A × C)
(iii) (A ∪ B) × C = (A × C) ∪ (B × C)
A ∪ B = {0, 1} ∪ {2,3,4}
= {0,1, 2, 3, 4}
(A ∪ B) × C = {0, 1,2, 3,4} × {3,5}
= {(0, 3) (0, 5) (1, 3) (1, 5)(2, 3) (2, 5) (3, 3)(3, 5) (4, 3)(4, 5)} ….(1)
A × C = {0, 1} × {3,5}
= {(0,3) (0,5) (1,3) (1,5)}
B × C = {2,3,4} × {3,5}
= {(2,3) (2,5) (3,3) (3,5)(4,3)(4,5)}
(A × C) ∪ (B × C) = {(0, 3) (0, 5) (1, 3) (1, 5) (2, 3)(2, 5) (3, 3) (3, 5) (4, 3) (4, 5)} ….(2)
From (1) and (2) we get
(A ∪ B) × C = (A × C) ∪ (B × C)
Maths Exercise 1.1 Class 10 Samacheer Question 7.
Let A = The set of all natural numbers less than 8, B = The set of all prime numbers less than 8, C = The set of even prime number. Verify that
(i) (A ∩ B) × c = (A × C) ∩ (B × C)
(ii) A × (B – C ) = (A × B) – (A × C)
A = {1, 2, 3, 4, 5, 6, 7}
B = {2, 3, 5, 7}
C = {2}
Solution:
(i)(A ∩ B) × C = (A × c) ∩ (B × C)
LHS = (A ∩ B) × C
A ∩ B = {2, 3, 5, 7}
(A ∩ B) × C = {(2, 2), (3, 2), (5, 2), (7, 2)} ………… (1)
RHS = (A × C) ∩ (B × C)
(A × C) = {(1, 2), (2, 2), (3, 2), (4, 2), (5, 2), (6, 2), (7, 2)}
(B × C) = {2, 2), (3, 2), (5, 2), (7, 2)}
(A × C) ∩ (B × C) = {(2, 2), (3, 2), (5, 2), (7, 2)} ……….. (2)
(1) = (2)
∴ LHS = RHS. Hence it is verified.
(ii) A × (B – C) = (A × B) – (A × C)
LHS = A × (B – C)
(B – C) = {3,5,7}
A × (B – C) = {(1, 3), (1, 5), (1, 7), (2, 3), (2, 5), (2, 7) , (3, 3), (3, 5), (3, 7), (4, 3), (4, 5), (4, 7), (5, 3), (5, 5), (5, 7), (6, 3) , (6, 5), (6, 7), (7, 3), (7, 5), (7, 7)} …………. (1)
RHS = (A × B) – (A × C)
(A × B) = {(1,2), (1,3), (1,5), (1,7),
(2, 2), (2, 3), (2, 5), (2, 7),
(3, 2), (3, 3), (3, 5), (3, 7),
(4, 2), (4, 3), (4, 5), (4, 7),
(5, 2), (5, 3), (5, 5), (5, 7),
(6, 2), (6, 3), (6, 5), (6, 7),
(7, 2), (7, 3), (7, 5), (7,7)}
(A × C) = {(1, 2), (2, 2),(3, 2),(4, 2), (5, 2), (6, 2), (7, 2)}
(A × B) – (A × C) = {(1, 3), (1, 5), (1, 7), (2, 3), (2, 5), (2, 7), (3, 3), (3, 5), (3, 7), (4, 3), (4, 5), (4, 7), (5, 3), (5, 5), (5, 7), (6, 3), (6, 5), (6, 7), (7, 3), (7, 5), (7,7) } ………….. (2)
(1) = (2) ⇒ LHS = RHS.
Hence it is verified. | 3,439 | 5,513 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5625 | 5 | CC-MAIN-2024-10 | latest | en | 0.784507 |
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Find the coordinates of either of the vertices of the hyperbola \(16x^2+16x-4y^2-20y-85=0\)
(Enter your answer as an ordered pair. Enter the coordinates of one of the vertices, not both.)
Find the distance between the foci of the ellipse x^2 + 4y^2 = 400.
May 8, 2019 | 99 | 283 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2020-05 | longest | en | 0.729088 |
https://www.physicsforums.com/threads/capture-in-a-two-body-system-by-gravitational-radiation.889247/ | 1,519,504,031,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891815934.81/warc/CC-MAIN-20180224191934-20180224211934-00681.warc.gz | 906,590,213 | 18,989 | # A Capture in a Two-Body System by Gravitational Radiation?
Tags:
1. Oct 15, 2016
### Yazzledore
Is it possible for enough energy to be dissipated in the form of gravitational radiation in a two-body system to allow for capture? From what I remember, you would need extremely massive bodies passing extremely close to each other: I'd like to know how massive and how close.
It has been a few years since I did any GR and don't feel confident in my ability to do the math anymore (but I think I can still understand it). If it is possible, I was hoping someone had seen a good paper to which they could link me (I couldn't find one).
2. Oct 15, 2016
### Staff: Mentor
I assume you mean a two-body system that does not start out bound. I haven't done the calculation, but I would guess that this is, while not impossible in principle, extremely unlikely. The time scale for gravitational radiation to carry significant energy away from a system is likely to be much longer than the time scale for a pair of unbound objects to swing past each other and escape.
The basic intuition here is that gravitational radiation requires many orbits to carry away significant energy. But for a pair of unbound objects passing each other, you only have one "orbit"--they pass once and then fly apart. It doesn't seem to me that gravitational radiation could do enough during that one brief passage. But, as I said, I haven't done the calculation.
3. Oct 15, 2016
### pervect
Staff Emeritus
I don't think you need gravitational radiation to have capture in a 2 body system in GR. Consider a test particle that falls from infinity and passes within the photon sphere of a black hole, for instance. The test particle can't orbit - no orbit exists inside the photon sphere - so it must be captured.
[add]And - a test particle follows a geodesic, it doesn't emit any gravitational radiation.
Last edited: Oct 15, 2016
4. Oct 15, 2016
Staff Emeritus
If the capture-ee comes in on a parabolic trajectory, if the system loses any energy at all the trajectory will become elliptical.
5. Oct 15, 2016
### Staff: Mentor
You don't. But the question I understand the OP to be asking is, given a scenario in which, leaving gravitational radiation out of account, the 2 body system would not result in capture, could the effects of gravitational radiation change that outcome so that there would be capture?
Following a geodesic is not a sufficient condition for not emitting gravitational radiation. The binary pulsars whose orbital decays have been used to confirm GR predictions of gravitational radiation are traveling on geodesic orbits.
Being a test particle, in itself, is a sufficient condition for not emitting gravitational radiation, however, because by definition a test particle cannot contribute at all to any system's gravitational properties, including those which cause gravitational radiation to be emitted (i.e., a time varying mass quadrupole moment).
6. Oct 16, 2016
### pervect
Staff Emeritus
It's getting a bit off topic, but do you have a reference for this point? I would think that the momentum and energy carried away by the gravitational radiation would cause departures of the non-test particle from a geodesic.
It's easy enough to come up with a test particle orbit that does not decay - if a massive body could follow the same non-decaying orbit and still emit gravitational radiation, I don't see how energy-at-infinity could be conserved.
7. Oct 16, 2016
### Staff: Mentor
I can try to dig one up, but AFAIK the models that generate the predictions for which Hulse and Taylor won the Nobel prize, and similar predictions for other binary pulsars, assume geodesic orbits, so the fact that they match the data so well is strong evidence that the binary pulsars are in fact traveling on geodesic orbits, at least to a very, very good approximation.
No, they just mean that the geodesics are geodesics of the full spacetime geometry including the effects of gravitational waves, rather than the geodesics of an idealized Schwarzschild geometry without gravitational waves, which are the kinds of orbits we intuitively think about when we think about orbiting objects.
Sure, if you ignore the effects of gravitational waves. But if you include those effects, the spacetime geometry is no longer Schwarzschild, so the non-decaying geodesic orbits you are intuitively thinking of no longer exist.
If, OTOH, you just mean that if all we have is one massive body with test particles orbiting it, there are no gravitational waves period and the geometry is just the static Schwarzschild geometry, that I agree with. But it's irrelevant to the case under discussion.
Which it can't. You are right that this would violate energy conservation. But the energy being conserved here is not what you appear to think it is. See below.
Energy at infinity is only a conserved quantity along a geodesic orbit if the spacetime is stationary. If gravitational waves are present, the spacetime is not stationary, so there is no such conserved quantity.
The only conserved energy in the case we are discussing, a spacetime with gravitational waves but which is still asymptotically flat, is the ADM energy of the spacetime as a whole. But that's not the same as energy at infinity for an orbiting object. If an object could follow a non-decaying geodesic orbit in a spacetime containing gravitational waves, then the ADM energy would not be conserved (heuristically, because the non-decaying orbit would be making a constant contribution to the ADM energy, while the gravitational waves would be making an increasing contribution--whereas if the orbit is decaying, its contribution to the ADM energy decreases, by the same amount that the gravitational wave contribution increases).
Last edited: Oct 16, 2016 | 1,266 | 5,820 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.84375 | 3 | CC-MAIN-2018-09 | longest | en | 0.960723 |
https://metanumbers.com/19809 | 1,624,385,364,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488519183.85/warc/CC-MAIN-20210622155328-20210622185328-00434.warc.gz | 356,293,101 | 10,889 | ## 19809
19,809 (nineteen thousand eight hundred nine) is an odd five-digits composite number following 19808 and preceding 19810. In scientific notation, it is written as 1.9809 × 104. The sum of its digits is 27. It has a total of 4 prime factors and 12 positive divisors. There are 12,600 positive integers (up to 19809) that are relatively prime to 19809.
## Basic properties
• Is Prime? No
• Number parity Odd
• Number length 5
• Sum of Digits 27
• Digital Root 9
## Name
Short name 19 thousand 809 nineteen thousand eight hundred nine
## Notation
Scientific notation 1.9809 × 104 19.809 × 103
## Prime Factorization of 19809
Prime Factorization 32 × 31 × 71
Composite number
Distinct Factors Total Factors Radical ω(n) 3 Total number of distinct prime factors Ω(n) 4 Total number of prime factors rad(n) 6603 Product of the distinct prime numbers λ(n) 1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 0 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0
The prime factorization of 19,809 is 32 × 31 × 71. Since it has a total of 4 prime factors, 19,809 is a composite number.
## Divisors of 19809
1, 3, 9, 31, 71, 93, 213, 279, 639, 2201, 6603, 19809
12 divisors
Even divisors 0 12 6 6
Total Divisors Sum of Divisors Aliquot Sum τ(n) 12 Total number of the positive divisors of n σ(n) 29952 Sum of all the positive divisors of n s(n) 10143 Sum of the proper positive divisors of n A(n) 2496 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 140.744 Returns the nth root of the product of n divisors H(n) 7.9363 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors
The number 19,809 can be divided by 12 positive divisors (out of which 0 are even, and 12 are odd). The sum of these divisors (counting 19,809) is 29,952, the average is 2,496.
## Other Arithmetic Functions (n = 19809)
1 φ(n) n
Euler Totient Carmichael Lambda Prime Pi φ(n) 12600 Total number of positive integers not greater than n that are coprime to n λ(n) 210 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 2247 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares
There are 12,600 positive integers (less than 19,809) that are coprime with 19,809. And there are approximately 2,247 prime numbers less than or equal to 19,809.
## Divisibility of 19809
m n mod m 2 3 4 5 6 7 8 9 1 0 1 4 3 6 1 0
The number 19,809 is divisible by 3 and 9.
## Classification of 19809
• Arithmetic
• Deficient
### Expressible via specific sums
• Polite
• Non-hypotenuse
## Base conversion (19809)
Base System Value
2 Binary 100110101100001
3 Ternary 1000011200
4 Quaternary 10311201
5 Quinary 1113214
6 Senary 231413
8 Octal 46541
10 Decimal 19809
12 Duodecimal b569
20 Vigesimal 29a9
36 Base36 fa9
## Basic calculations (n = 19809)
### Multiplication
n×i
n×2 39618 59427 79236 99045
### Division
ni
n⁄2 9904.5 6603 4952.25 3961.8
### Exponentiation
ni
n2 392396481 7772981892129 153974998301183361 3050090741348141198049
### Nth Root
i√n
2√n 140.744 27.0575 11.8636 7.2339
## 19809 as geometric shapes
### Circle
Diameter 39618 124464 1.23275e+09
### Sphere
Volume 3.25594e+13 4.931e+09 124464
### Square
Length = n
Perimeter 79236 3.92396e+08 28014.2
### Cube
Length = n
Surface area 2.35438e+09 7.77298e+12 34310.2
### Equilateral Triangle
Length = n
Perimeter 59427 1.69913e+08 17155.1
### Triangular Pyramid
Length = n
Surface area 6.79651e+08 9.16055e+11 16174
## Cryptographic Hash Functions
md5 32f57b05e13cc66c536619f3cda36b39 9a0c475ee37c101bb469d63d068d7cb0868616f0 bb85e20b14b56ae3624ab38461460c624d381530f13c83910da4b32dc43b42e4 1d9f3e3233d68f6c7ef62713a085bffb145aefb143700d3c69aff27fc83e20e1b03047265ad245d1b57db2e53e8f95a52f4e172cb9a6d77e0629203ea4427c68 21ee8e8a965efdd978278aa83c652c19eff254de | 1,467 | 4,136 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.703125 | 4 | CC-MAIN-2021-25 | latest | en | 0.812454 |
https://www.physicsforums.com/search/2055357/ | 1,597,139,995,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439738746.41/warc/CC-MAIN-20200811090050-20200811120050-00229.warc.gz | 779,534,271 | 15,276 | # Search results
1. ### Help to understand Newtons Law
Homework Statement I am trying to understand a diagram I have of a gymnast hanging from a bar. She weighs 50kg and is not swinging, just hanging. In the diagram it has her weight as 500N (using 10/m/s/s for gravity * 50kg) but the bar she is hanging from has an upward arrow with 550 N next to...
2. ### How is math education in the US structured ? Pre algebra , calc etc
I was trying to establish form high school up to the pint where you are about to start university, in what order are the maths classes taught. where I live they are just taught as level 1, 2 and 3. But I left school long before these were introduced so have idea what they refer to.
3. ### How is math education in the US structured ? Pre algebra , calc etc
I wanting to do some papers at university, however I have long been out of high school and never really don math or science at high school. As an adult I am now keen to pursue some math papers and was wondering what kind of background I need. I have looked through various web pages and they...
4. ### Learning maths concepts …not just how to do an equation
I tried posting in the education section but was unable to start a topic… Anyways…I'm trying to reteach myself maths from back in the school days in hope of doing a calculus paper at university. I have realized that a lot of books and materials seem to teach you how so l've equations and...
5. ### Re-learning math (books?)
I'm in a similar situation, in that I have gone to learning maths again as an adult and while the odd piece of maths form here and there has stuck with me, I often can just plug in numbers to a formula and get an answer. ..BUT…if you asked me why it worked that way I'd be stumped and possibly...
6. ### How do derivatives provide answers for optimization problems ?
I' at a a very very very basic level of calculus and usually have to watch a video or read something basic just to understand the basics. I'm fascinated by optimization equations, for example what is the largest area that can made with 500m of fencing. So at some point in solving this we end...
7. ### Archived Help with internal moments = external moments
Homework Statement Internal moments need to equal external moments, work out the total of the internal moments. The object has a mass of 2 kg Homework Equations I have obtained the moment about I (labelled as MI) + Iα The Attempt at a Solution the moment about I (MI)...
8. ### How to find forces acting on object on a slope?
here is my latest diagram I'm now starting to think Soh Cah Toa isn't actually relevant there ? Fn = G cosσ Ft = Gσ I'm unsure where these two formulas/equations have come from and why Soh Cah Toa isn't relevant here... I must be missing something fundamental
9. ### How to find forces acting on object on a slope?
Thanks NascentOxygen. Unfortunately I dont quite get why the answers are what they are. I have drawn myself a new triangle which shows the two vector forces but I still don't understand where the answers have come from. Especially Fn = G cosσ. I thought cos in basic terms meant...
10. ### How to find forces acting on object on a slope?
edited...I'll be back
11. ### How to find forces acting on object on a slope?
Homework Statement an object is at rest on a slope at angle of σ Using trigonometry, solve the forces acting at Ft and Fn Homework Equations Soh Cah Toa The Attempt at a Solution sin σ = G/Ft sin σ /Ft = G G/ sin σ = Ft (my final answer) Book says correct answer is Ft = G sinσ...
12. ### Torque, rotational inertia and angular acceleartion
what happens though if the body isn't rotating and I want to start it rotating but can't apply enough force to do so ? I'm still applying torque though ....aren't I ?
13. ### Torque, rotational inertia and angular acceleartion
Homework Statement In order to link these into a logical sequence, how do they fit together Homework Equations I = rotational inertia a = angular acceleration (I know a different symbol is usually used) τ= force x moment arm distance The Attempt at a Solution so....to...
14. ### What is Torque and what is correct formula?
I'm struggling with the concept of torque as I read more I get further confused. I read some sources and they say torque and moments are interchangeable, yet other sources make a specific effort to keep the two separate. So question one is , what is the difference between torque and a moment...
15. ### Delta V/ delta t vs. dv/dt
I know delta means change , but I don't what the difference between Δv/Δt vs dv/dt is ? I am at the noob end of calculus so trying to grasp how to interpret things like dv/dt or what what dv would mean if it were standing alone. TIA
16. ### Help understanding class content and keeping up
This may be the wrong section , but I figure it was education relevant. In class I can't always keep up with the current lecture, but then when it starts incorporating previous lectures and the principles I can find it even harder to keep up. I notice some students can start to piece it...
17. ### Position - time graph
I think that is correct, the slope at that particular point is your velocity.
18. ### What does the area under a Distance vs Time graph indicate
Homework Statement Given a graph with distance (in meters) on the y axis and time (in seconds) on the x axis what does the area under this graph illustrate ? The object has a velocity of 1m/s so after 5 s it has travelled 5m. Homework Equations This is a linear line (i.e y=x) so the area...
19. ### Why is W=m*g relevant if I am standing still and not moving ?
Thanks for the help with this.....much appreciated. Still trying to get my head around the F=m*a is equivalent to W= m*g statement. So this is not true then (in the case where I am standing still on the footpath) If I am not accelerating to the center of the earth due to the force of the...
20. ### Why is W=m*g relevant if I am standing still and not moving ?
Homework Statement Why is gravity still 9.81m/s/s when we are standing still ? and why do I have a weight when I am standing still ? Homework Equations F=m*a W=m * g a= (final velocity - initial velocity)/ time The Attempt at a Solution So it requires more of a theory...
21. ### Help understanding this Kinetic energy problem
although I dont understand the question properly , they did say in ithe question the skater does 300J of work, so it looks liek you'd be on the right track rcgld "By my math, the skater does about 296.37728 J of work." I just have no ideas if my answers are on the right path or not.
22. ### Help understanding this Kinetic energy problem
Homework Statement A 60kg ice skater is spinning around at 300 degrees per second. His radius of gyration is .5m. As he pulls his arms in he does 300 J of work. i.What is his initial kinetic energy? ii.What is his final kinetic energy ? iii.Assuming that his new radius of gyration is .32m...
23. ### Impulse and momentum question, relates to Biomechanics
yes this is where I'm confused...how do you incorporate g into it ?
24. ### Impulse and momentum question, relates to Biomechanics
to the best of my knowledge yes, I have literally written out the question as it was presented.
25. ### Impulse and momentum question, relates to Biomechanics
Homework Statement A male and female pair of dancers start dancing when the male lifts the female and throws her into the air. The female's mass is 40kg . The male exerts an average vertical force of 500n for 1.0s on the female. What is her vertical velocity when she is released into the air...
26. ### Buoyant force in seawater and freshwater
ohh I'm definitely confused.... oli4 makes mention of the fact that if I submerge an object in freshwater or seawater then the volume displaced will be identical. I believe this is due to the fact that the object has been submerged. I guess it's different in the case of a boat floating ? In...
27. ### Buoyant force in seawater and freshwater
Homework Statement I'm doing a problem that is likely a common one. It is comparing the buoyant force of an object in seawater to that of the same object in freshwater. which has more buoyant force acting on it? Homework Equations not sure of equations at this stage, and we are just...
28. ### Help understanding dynamic equilibrium
hmmm I dont quite get what would make the box slide ? If ƩF=0 and there's no friction my guess would be there is no force...but then I don't get how the box would be sliding with no force on it
29. ### Help understanding dynamic equilibrium
Homework Statement if the equilibrium rule states ƩF=0N, how can something move or be moving at a constant speed ? eg I push on a box with 50N and friction provides 50N back, resulting in ƩF=0N. So I am not providing more N than the box is resisting with. I thought something could only be...
30. ### What is the point of angling projectiles?
Homework Statement If the horizontal velocity remains the same, whether angled or not, I dont quite understand why we bother launching projectiles upwards on an angle? Would it be better just to launch them horizontally ? Homework Equations d= 1/2gt^2....I think? The Attempt at... | 2,139 | 9,183 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.921875 | 3 | CC-MAIN-2020-34 | latest | en | 0.977227 |
http://www.expertsmind.com/questions/how-is-specific-gravity-defined-30187222.aspx | 1,638,638,728,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964362999.66/warc/CC-MAIN-20211204154554-20211204184554-00582.warc.gz | 101,847,576 | 12,886 | ## How is specific gravity defined, Physics
Assignment Help:
How is Specific Gravity defined?
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A boat travels 75 km southeast, then 56 km due east, then 25 km 30.0° north of east. a. Sketch the vector set on a N-E-S-W grid b. Find its net E-W part of displacement and | 597 | 2,700 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2021-49 | latest | en | 0.880308 |
https://www.atlaspm.com/toms-tutorials-for-excel/tom-s-tutorials-for-excel-viewing-all-worksheets-with-one-indirect-formula/?replytocom=93711 | 1,600,886,450,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400212039.16/warc/CC-MAIN-20200923175652-20200923205652-00129.warc.gz | 687,190,484 | 13,842 | # Tom’s Tutorials For Excel: Viewing All Worksheets With One INDIRECT Formula
Tom’s Tutorials For Excel: Viewing All Worksheets With One INDIRECT Formula
Here’s how you can use Data Validation with the `INDIRECT` function in a single formula to quickly and easily view the contents of other worksheets in your workbook.
Suppose your workbook is the company budget, designed so the company’s regions occupy their own budget worksheets. For example, the following picture shows worksheets for North, South, East, and West regions. A Summary worksheet is also designed the same, and is the focus of this example.
Step 1
On the Summary worksheet in cell H2, Data Validation is applied, with the list of allowable entries limited to the regions’ worksheet tab names. I selected cell H2 and pressed `Alt+D+L` to show the Data Validation dialog box. In the Source field for List, I typed in those tab names separated by a comma, as shown in the following picture.
Step 2
Still on the Summary worksheet, I selected the same range of cells that contain budget numbers for the other regions. It’s a valuable benefit from designing the workbook with all worksheets laid out the same. In the active cell (B4 in this example) I typed the formula…
`=IF(LEN(\$H\$2)=0,0,INDIRECT("'"&\$H\$2&"'!"&ADDRESS(ROW(),COLUMN())))`
…and I pressed `Ctrl+Enter` which applied that formula to all selected cells.
Step 3
Now while never leaving the Summary worksheet, it’s a simple matter of selecting the worksheet name from the drop down list in cell H2 depending on which region I want to quickly see. In the following picture, I selected the East Region.
Here are the East Region’s numbers.
###### 10 comments on “Tom’s Tutorials For Excel: Viewing All Worksheets With One INDIRECT Formula”
1. chander says:
Can we use this formula if we have 120 bank accounts (sheets)..?
• Phil says:
Hi chander,
I don’t know why this shouldn’t work the same way with 120 bank accounts. It surely is a little bit more work than “just” four regions but should be possible (with a little 😉 more work).
Hope that helps
Phil
2. Bart says:
Hi Tom, I have a workbook wherein a consecutive range of sheets are named differently (in particular each sheet is a person’s name.) Now, from time to time a sheet may be added or deleted within the range of sheets. I need a formula that lists the content of the same single cell on each sheet in a column on another sheet. Can you please help?
• Tom Urtis says:
Try inserting two dummy sheets. Name them start and end. Put all the sheets you’re interested in between the start and end sheets. Sum of interest (for example, cell A1) would be this formula:
=sum(start:end!A1)
3. Robert says:
Hi Tom, I have a workbook where each sheet is named differently and I want to pull the data from the same cell on each page. Currently my summary sheet is listed in this way (see below), (where “1001” is the name of the worksheet, and so forth). I am wanting to set up my summary page so that each time a new worksheet is added, the summary page adds a new row and pulls the info. So if I open up sheet “1250” and put data into D5, then when I go back to the summary page, it shows a new row with the date from that worksheet.
‘1001’!D5
‘1002’!D5
‘1003’!D5
Thanks for any help if you still read this.
• Tom Urtis says:
Questions:
(1)
Is the name of the summary worksheet really “Summary”?
(2)
Are there other worksheet besides the summary sheet whose cell D5 would not be included in the calculation, and if so, what are those non-inclusive sheets’ names?
(3)
When you say “the summary page adds a new row”, that to me means the solution should be VBA, not strictly a formula, so is that OK. If it is not OK to use VBA, then I would not suggest a strict formula solution because it would not be robust enough to be effective.
4. Sauvanik says:
Is there anyway to do this if the tab names keep changing? The individual tab names change using a vba that makes the tab name change to whatever i typed in to cell A1 of that sheet.
• Tom Urtis says:
There are 2 other ways to do this. One is by using the INDEX function but that can also bring you problems depending on the order in which the sheets are arranged relative to each other. I almost never use the INDEX property to reference a worksheet.
The most reliable way to do this is with a macro or user-defined function to refer to the worksheets’ CodeName property, which never changes no matter what the sheet tab name is, or who is using the workbook, or which position the worksheet is in relative to other worksheets. This would require VBA so if that is not an option for you then you are destined to have problems referring to worksheets when their names and positions change. If you know that a VBA solution is OK, then post back saying so and we can take it from there.
5. ammie says:
I am looking for help to a similar problem.
I would like to return the information in the same cell in multiple worksheets. Each worksheet is numbered 1, 2, 3, etc. and in the summary tab I am looking to populate the table rows are labeled 1, 2, 3, etc. What formula can I used that references the numbers in the table as the look up for the sheet I want the numbers populated from?
Eg.
Week Data
1 (from cell K13 on sheet 1)
2 (from cell K13 on sheet 2)
3 (from cell K13 on sheet 3)
4 (from cell K13 on sheet 4)
etc
6. ammie says:
I am looking for help to a similar problem.
I would like to return the information in the same cell in multiple worksheets. Each worksheet is numbered 1, 2, 3, etc. and in the summary tab I am looking to populate the table rows are labeled 1, 2, 3, etc. What formula can I used that references the numbers in the table as the look up for the sheet I want the numbers populated from?
Eg.
Week Data
1 (from cell K13 on sheet 1)
2 (from cell K13 on sheet 2)
3 (from cell K13 on sheet 3)
4 (from cell K13 on sheet 4)
etc
Thank you for helping to look into this.
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# Topic: List of equations
###### In the News (Tue 22 May 18)
Maxima Manual: 21. Equations Solves the list of simultaneous linear equations for the list of variables. The first list represents the equations to be solved; the second list is a list of the unknowns to be determined. If the total number of variables in the equations is equal to the number of equations, the second argument-list may be omitted. maxima.sourceforge.net /docs/manual/en/maxima_21.html (1715 words)
Encyclopedia: List of equations Mathematical lists The advection equation is the partial differential equation that governs the motion of a conserved scalar as it is advected by a known velocity field. The primitive equations are a version of the Navier-Stokes equations which describe hydrodynamical flow on the sphere under the assumptions that vertical motion is much smaller than horizontal motion (hydrostasis) and that the fluid layer depth is small compared to the radius of the sphere. Einstein's famous equations says that mass m is equivalent to energy E, and the amount of energy contained in a piece of mass is equal to the mass multiplied with the square of the speed of light, c. www.nationmaster.com /encyclopedia/List-of-equations (2646 words)
[No title] Equations (4-1) through (4-7) are used to calculate the linearized continuum magnitude at each of the HB filter wavelengths. Absolute fluxes are obtained using: equations (5-1) through (5-4) for the continuum filter measurements, equations (6-1) through (6-7) for the interpolated continuum under the gas species, and equations (7-1) through (7-7) for the measurements with the gas filters themselves. The required list indicates that a measurement in at least one of the listed filters is necessary for proper continuum determination. www.lowell.edu /Research/Projects/comet-filters/hbfilters/reduc_instr.txt (2435 words)
Gaussian Elimination (Site not responding. Last check: 2007-10-13) Note that this set of equations has a special form: it has a triangle in the lower left corner in which all coefficients are zero. The returned equations have the same solutions as the original equations, except they are in triangular form. loe) empty] [else (local [(define rest-sols (solve (map rest (rest loe)))) (define const-eqn (subst rest-sols (rest (first loe))))] (cons (/ (eval const-eqn) (first (first loe))) rest-sols))])) ;; eval : (nelistof number) -> number ;; solves sum of constants where last number is on right-hand side and ;; all other numbers are on left-hand side. www.owlnet.rice.edu /~comp210/99fall/Lectures/22.shtml (693 words)
GMM The instrument list may be different for each equation (see the MASK option or the INST option) and the form of the covariance matrix used for weighting the estimator is under user control (the HETERO option for heteroskedastic-consistency and the NMA= option for moving average disturbances). List the instruments in the INST= option and list the equations after the options; the products of these two are the orthogonality conditions, which are minimized in the metric of an estimate of their expected covariance. The matrix is # of instruments by # of equations and the default is a matrix of ones (all instruments used for all equations). www.tspintl.com /products/tsphelp/gmm.htm (1171 words)
Out.Equat11 In equation 1 the variables y and x are raised to the first power (1), while in equation 7 x is raised to the second power (2). Equation 3, meanwhile, does satisfy our condition for a linear relationship, the only difference is that y depends on two exogenous variables, x and z. In the linear equation, if we are at x = 1 and z = 2 and move to x = 2, then y increases by 4. www.uri.edu /artsci/ecn/mead/306a/Outlines/Algebra/Out.Equat11.html (802 words)
Using a Mathematica Notebook The Solve function takes up to two arguments, a list of equations and an optional list of variables for which to solve. In this example, only the list of equations is used. Like all lists, the list of equations is surrounded by {...}. www.cae.wisc.edu /site/public/print.php?title=usingmathnote (473 words)
List of relativistic equations - Wikipedia, the free encyclopedia The following definitions and equations should be applied to any situation when the speed of an observer or object is greater than one tenth of the speed of light. In modern treatments of special relativity, mass is always defined as the mass measured by a comoving observer, and is therefore synonymous with the rest mass. This article contains only a very few of the definitional equations of the Theory of relativity. en.wikipedia.org /wiki/List_of_relativistic_equations (364 words)
Importing equations and the equation library When you select an equation from the library, you transfer it from the library file to your own list of equations. Prism stores the equation with every file that uses it, and also places the equation in your list of user-defined equations (the list you see when you choose "more equations"). When you import an equation, you transfer to your own list of equations (the list you see when you choose "more equations"). www.graphpad.com /curvefit/importing_equations_.htm (509 words)
Calculating Derivatives with Mathematica The first argument to D is the equation or list of equations the are to be differentiated. These equations were inclosed in brackets so that they would both be seen as part of the first argument. The first argument is the equation to be integrated while the second is the variable that the integration is to be in respect to. www.cs.princeton.edu /courses/archive/fall99/cs323/precepts/differential/math.html (260 words)
Equations and Expressions Equations can be created that contain variables as well as one or more expressions (i.e., equation sets). A sketch equation is one that resides in and is always associated with the sketch that is active at the time it is created. This supports the "family-of-parts" concept by allowing equation sets to be externally driven by a tabulated list of variables and their values or by equations. www.vx.com /help/0398.htm (3147 words)
Manage Equations Equation: This is a list of the equations available in the present session of the response viewer. Any equations that you have previously defined and saved in an equation file may be loaded into the present session of the response viewer. View Equation dialog box which allows you to view all the fields entered for this equation but does not allow you to modify them. www.sonnetusa.com /support/help-v11/dialog_boxes/manage_equations.htm (853 words)
Userdefined equations If you enter a discontinuous equation (where an infinitesimal change in X can create a huge change in Y) the results of nonlinear regression may not be reliable. For each variable in the equation, enter a number in the first column and select a multiplier from the drop-down list in the second column. When you pick one of those files, it shows a list of all user-defined equations used in the file, along with a thumbnail preview of the first graph linked to each equation. www.curvefit.com /writing_equations.htm (1398 words)
The equations below will be provided on the exam as shown below (Site not responding. Last check: 2007-10-13) You should make sure you understand the concepts embodied in each of these equations and thus the conditions under which they apply. These equations are all from chapters 8 and 9. There are additional equations you are responsible for (law of mass action for instance), but I believe that people have a grasp of them from their work prior to the midterm. www.uoregon.edu /~ch225/equations.htm (123 words)
Importing equations and the equation library When you select an equation from the library, you transfer it from the library file to your own list of equations. Prism stores the equation with every file that uses it, and also places the equation in your list of user-defined equations (the list you see when you choose "more equations"). When you import an equation, you transfer to your own list of equations (the list you see when you choose "more equations"). www.curvefit.com /importing_equations_.htm (509 words)
Solving Equations There are some equations, however, for which it is mathematically impossible to find explicit formulas for the solutions. You simply give the list of equations, and specify the list of variables to solve for. When you are working with sets of equations in several variables, it is often convenient to reorganize the equations by eliminating some variables between them. documents.wolfram.com /v4/MainBook/1.5.7.html (638 words)
List of relativistic equations - Encyclopedia, History, Geography and Biography List of relativistic equations - Encyclopedia, History, Geography and Biography Special Relativity was put forth by Albert Einstein and is possibly his most famous contribution to science. List of relativistic equations, Special relativistic equations, Definitions, Equations, See also, Further reading, Special relativistic equations, Definitions, Equations, See also, Further reading, Special relativity, Equations and Physics lists. www.arikah.com /encyclopedia/List_of_relativistic_equations (446 words)
Encyclopedia: List of relativistic equations Note that at one time in presentations of special relativity, it was common to introduce a quantity called the relativistic mass, defined as m=γm An equation for the characteristic surface (characterizing the propagation of disturbances under the double simple wave restriction) is constructed. Similar to the nonrelativistic case, the equation for vn is shown to be formally like a new charged fluid but (unlike the nonrelativistic flow) with a new formal thermodynamics. www.nationmaster.com /encyclopedia/List-of-relativistic-equations (201 words)
List of equations - Encyclopedia, History, Geography and Biography List of equations - Encyclopedia, History, Geography and Biography This encyclopedia, history, geography and biography article about List of equations contains research on List of equations, Named equations, Other equations, Equations, Differential equations and Mathematical lists. www.arikah.net /encyclopedia/List_of_equations (87 words)
MODEL MODEL takes as its arguments the name of a list of equations in the model, and produces a collected and ordered model which is stored under the name supplied by the user. Each of the endogenous variables in the list must appear on the left hand side of one and only one of the equations. A table is printed which shows for each equation in the model the number of its block, whether the block is simultaneous (S) or recursive (R), and which endogenous variables appear in that equation. www.tspintl.com /products/tsphelp/model.htm (423 words)
101Systems of Equations.lbz A system of linear equations is a list of m linear equations in a common set of variables If we replace the second equation by the original second equation minus the first, the system of equations changes, but the solution does not. If we were to stop at this point and convert the augmented matrix back into a system of equations, we would have an upper-triangular system of equations that could be solved by back-substitution. www.lawrence.edu /fast/greggj/CMSC110/Gauss/Gauss.html (1226 words)
Substituting Expressions (Site not responding. Last check: 2007-10-13) The substitutions are made in the order given by the list of equations, that is, from left to right. That is, the first argument may be a single substitution equation or a list of such equations, while the second argument is the expression being processed. If the last argument to a part function is a list of indices then several subexpressions are picked out, each one corresponding to an index of the list. starship.python.net /crew/mike/maxima/html/macref/node34.html (449 words)
Vision Engineer - Reference: List of Equations (Site not responding. Last check: 2007-10-13) Having said that, equations are nothing more than simple expressions that relate physical phenomeon. Lamé equations are used to calculate hoop and radial stresses in cylinders. The equation of state applies to ideal gases and relates pressure and temperature. www.visionengineer.com /ref/equations.php (186 words)
Maxwell's Equations (Site not responding. Last check: 2007-10-13) These basic equations of electricity and magnetism can be used as a starting point for advanced courses, but are usually first encountered as unifying equations after the study of electrical and magnetic phenomena. Maxwell Equations -- from Eric Weinstein's World of Physics: This is a set of Maxwell's equations using partial derivatives. Maxwell's Equations: Proof: This is a proof of Maxwell's equations how they came to be. www.personal.psu.edu /users/f/z/fzs100/myweb2/new_page_13.htm (96 words)
RIES - Find Algebraic Equations, Given Their Solution at MROB It should also be apparent that the simplest equations come first and the more complex ones later on. ries follows the example of continued fractions — as you go to longer equations, you get a closer approximaion to your number, and each approximation is the closest approximation that is available with an equation of that complexity. equations in 62 seconds and uses 115 megs of memory. home.earthlink.net /~mrob/pub/ries (599 words)
List of equations (Site not responding. Last check: 2007-10-13) Charles Seife The Clay Institute announces a list of mathematical puzzles for the 21st century--at... their results in ordinary differential equations and Diophantine geometry, one of the few problems on Hilbert's list to remain unsolved. The effects of sample size and proportion of buyers in the sample on performance of list segmentation equations generate... hallencyclopedia.com /List_of_equations (325 words)
The Bart-Gohberg-Kaashoek-Van Dooren Theorem: Step 1 We run NCProcess1 for 2 iterations where the input is the equations FAC, together with the declaration of A, B, C as knowns and the remaining variables as unknowns. The spreadsheet created by NCProcess1 is a list of equations whose solution set is the same as the solution set for the FAC equations. First notice that the first equation is not written as a rule since it has a collected form. math.ucsd.edu /~ncalg/prod/prod1.html (261 words)
FC++ lazy list implementation (Site not responding. Last check: 2007-10-13) As of v1.3, lists have been completely reimplemented in a way that is far more efficient than the previous implementation. This document describes the new list implementation structure, and how you can write functoids to take advantage of the new structure to be more efficient. However, the "odd" lists described in that paper always evaluate "one too far ahead" in a list, whereas FC++'s OddLists effectively have "even" tails, which means only the original call is too eager; the recursive calls are fine. www.cc.gatech.edu /~yannis/fc++/New/new_list_implementation.html (1014 words)
The equations below will be provided on the exam as shown below The equations below will be provided on the exam as shown below (no annotation). These equations are all from chapters 8 and 9. There are additional equations you are responsible for (law of mass action for instance), but I believe that people have a grasp of them from their work prior to the midterm. darkwing.uoregon.edu /~ch225/equations.htm (123 words)
Autoregressive Moving Average Error Processes If the endolist is not specified, the endogenous list defaults to name, which must be the name of the equation to which the AR error process is to be applied. specifies the list of equations whose lagged structural residuals are to be included as regressors in the equations in eqlist. specifies the list of equations to which the MA process is to be applied. www.otago.ac.nz /sas/ets/chap14/sect49.htm (3387 words)
UBC ATSC/GEOG 201 Equations Below is a list of equations from the Stull textbook that will be covered. These are the equations that you are responsible for understanding and knowing how to use, for homework and exams. For those of you who took ATSC/GEOG 200, also listed are the equations that were already covered in that course, and the new topics that will be covered beyond that course. www.geog.ubc.ca /courses/geog201/G201Eqs.html (548 words)
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## String theory - Simple English Wikipedia, the free encyclopedia
simple.wikipedia.org/wiki/String_theory
String theory is a set of attempts to model the four known fundamental ... By the equivalence principle, Einstein inferred that being under either gravitation or ...
## String Theory Basics - The Official String Theory Web Site
superstringtheory.com/basics/
Here are the past successes of theoretical physics, from electromagnetism to particle physics and general relativity... basic / advanced ...
## The Basic Elements of String Theory - For Dummies
www.dummies.com/how-to/content/the-basic-elements-of-string-theory.html
Five key ideas are at the heart of string theory. Become familiar with these key elements of string theory right off the bat. Read on for the very basics of these five .
## What is String Theory ?
www.nuclecu.unam.mx/~alberto/physics/string.html
String theory is our most recent attempt to answer the last (and part of the second ) ... The electron is a truly fundamental particle (it is one of a family of particles ...
## String Theory for Kids (and Clever Adults) | String theory explained ...
stringtheory4kids.wordpress.com/
Jun 15, 2011 ... String theory explained for kids, teens, and even adults. ... We would know what is most basic and how everything else is composed of these basic ..... People have made up millions of such beliefs and many more will follow.
## Beyond string theory : strings
www.phys.ens.fr/~troost/beyondstringtheory/string.html
That contradiction in the basic assumptions of the theories proves difficult to get ... What are then the surprisingly new principles that string theory is based on ?
## A Layman's Guide To String Theory - Zidbits
zidbits.com/2011/03/a-laymans-explanation-for-string-theory/
Mar 19, 2011 ... What is string theory and why is it so hyped? ... models which seek to find a common explanation for the four main forces seen in nature. .... My problem with string theory is that I can't find any explanation of first principles.
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## Is String Theory Science? - Scientific American
www.scientificamerican.com/article/is-string-theory-science/
Dec 23, 2015 ... “Faced with difficulties in applying fundamental theories to the observed ... He classified string theory as testable “in principle” and thus perfectly ...
## M-Theory: The Mother of all SuperStrings : Explorations in Science ...
mkaku.org/home/articles/m-theory-the-mother-of-all-superstrings/
Every decade or so, a stunning breakthrough in string theory sends shock ..... feels that the key to solving string theory is to understand the under- lying principle ...
### String Theory For Dummies Cheat Sheet - For Dummies
www.dummies.com
The key string theory features include: ... The holographic principle, which states how information in a space can relate to information on the surface of that space ...
### What is String Theory? – Uncertain Principles - ScienceBlogs
scienceblogs.com
Aug 26, 2007 ... Free field theories have the property that the solutions can be expressed in terms of fundamental solutions which we can think of as particles.
### The Theory of Strings: A Detailed Introduction: Sunil Mukhi
theory.tifr.res.in
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# SalasSV_08_08_ex - 502 CHAPTER 8 TECHNIQUES OF INTEGRATION...
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EXERCISES *8.8 Determine whether the functions satisfy the differential equation. 1. 2 y y = 0; y 1 ( x ) = e x / 2 , y 2 ( x ) = x 2 + 2 e x / 2 . 2. y + xy = x ; y 1 ( x ) = e x 2 / 2 , y 2 ( x ) = 1 + Ce x 2 / 2 , 3. y + y = y 2 ; y 1 ( x ) = 1 e x + 1 , y 2 ( x ) = 1 C e x + 1 , 4. y + 4 y = 0; y 1 ( x ) = 2 sin 2 x , y 2 ( x ) = 2 cos x . 5. y 4 y = 0; y 1 ( x ) = e 2 x , y 2 ( x ) = C sinh 2 x , 6. y 2 y 3 y = 7 e 3 x ; y 1 ( x ) = e x + 2 e 3 x , y 2 ( x ) = 7 4 xe 3 x . Find the general solution. 7. y 2 y = 1. 8. xy 2 y = − x . 9. 2 y + 5 y = 2. 10. y y = − 2 e x . 11. y 2 y = 1 2 x . 12. xy + 2 y = cos x x . 13. xy 4 y = − 2 nx . 14. y + y = 2 + 2 x . 15. y e x y = 0. 16. y y = e x . 17. (1 + e x ) y + y = 1. 18. xy + y = (1 + x ) e x . 19. y + 2 xy = x e x 2 . 20. xy y = 2 x ln x . 21. y + 2 x + 1 y = 0. 22. y + 2 x + 1 y = ( x + 1) 5 / 2 . Find the particular solution determined by the initial condition. 23. y + y = x , y (0) = 1. 24. y y = e 2 x , y (1) = 1. 25. y + y = 1 1 + e x , y (0) = e . 26. y + y = 1 1 + 2 e x , y (0) = e . 27. xy 2 y = x 3 e x , y (1) = 0. 28. xy + 2 y = x e x , y (1) = − 1. 29. Find all functions that satisfy the differential equation y y = y y . HINT: Set z = y y . 30. Find the general solution of y + ry = 0 on [0, ) where r is a constant. (a) Show that if y is a solution and y ( a ) = 0 at some number a 0, then y ( x ) = 0 for all x . (A solution y is either identically zero or never zero.)
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8.8 DIFFERENTIAL EQUATIONS; FIRST-ORDER LINEAR EQUATIONS 503 (b) Show that if r < 0, then all nonzero solutions are unbounded. (c) Show that if r > 0, then all solutions have limit 0 as x → ∞ . (d) Describe all solutions of the equation in the case r = 0. Exercises 31 and 32 are concerned with the first-order linear differential equation ( ) y + p ( x ) y = 0 where the function p is continuous on an interval I . 31. (a) Show that if y 1 and y 2 are solutions of ( ), then u = y 1 + y 2 is also a solution of ( ). (b) Show that if y is a solution of ( ) and C is a constant, then u = Cy is also a solution of ( ).
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# Abstract Classes Polymorphism problem solution in C++ programming | HackerRank
#include <iostream>
#include <vector>
#include <map>
#include <string>
#include <algorithm>
#include <set>
#include <cassert>
using namespace std;
struct Node{
Node* next;
Node* prev;
int value;
int key;
Node(Node* p, Node* n, int k, int val):prev(p),next(n),key(k),value(val){};
Node(int k, int val):prev(NULL),next(NULL),key(k),value(val){};
};
class Cache{
protected
map<int,Node*> mp; //map the key to the node in the linked list
int cp; //capacity
Node* tail; // double linked list tail pointer
virtual void set(intint) = 0//set function
virtual int get(int) = 0//get function
};
#include <iostream>...
#include <list>
#define key first
#define val second
class LRUCache {
int cp;
map<int, list<pair<intint> >::iterator> mp;
list<pair<intint> > lru;
public:
LRUCache(int capacity) : cp(capacity){}
void set(int key, int val) {
if(mp.find(key) != mp.end()) {
mp[key]->key = key;
mp[key]->val = val;
}
else {
lru.push_front({key, val});
mp[key] = lru.begin();
if(lru.size() > cp) {
mp.erase(lru.back().key);
lru.pop_back();
}
}
}
int get(int key) {
if(mp.find(key) != mp.end()) {
lru.push_front(*mp[key]);
lru.erase(mp[key]);
mp[key] = lru.begin();
return mp[key]->val;
}
else
return -1;
}
};
int main() {
int n, capacity,i;
cin >> n >> capacity;
LRUCache l(capacity);
for(i=0;i<n;i++) {
string command;
cin >> command;
if(command == "get") {
int key;
cin >> key;
cout << l.get(key) << endl;
}
else if(command == "set") {
int key, value;
cin >> key >> value;
l.set(key,value);
}
}
return 0;
} | 716 | 2,113 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2020-40 | latest | en | 0.087433 |
https://www.physicsforums.com/threads/radioactive-decay-analyzing-1000-events-at-5-risk-level.793284/ | 1,709,434,240,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947476180.67/warc/CC-MAIN-20240303011622-20240303041622-00155.warc.gz | 942,845,131 | 17,645 | # Radioactive Decay: Analyzing 1000 Events at 5% Risk Level
• skrat
In summary, the experiment shows that out of 1000 events, 30% have a time between two consecutive events longer than 1 second and 5% have a time longer than 2 seconds. Using the theory of radioactive decay, the predicted numbers for these intervals are 63.21%, 23.2%, and 13.5% respectively. The calculated chi-squared value of 73.9 exceeds the expected value of 5.9915, indicating that the hypothesis of a 1-second decay time cannot be denied at a 5% risk level.
## Homework Statement
Analyzing 1000 events (each event is one radioactive decay of an unknown sample), we notice that the time between two consecutive events is larger than 1 second in 30% of the cases while in 5% it is longer than 2 seconds. Can we, at 5% risk level deny the hypothesis, that the characteristic decay time is 1 second long?
## The Attempt at a Solution
I really don't know how to begin here. I really don't. I do assume that I will have to use either Student distribution or Chi-squared distribution. But I have no idea how to start and what to do :/
Which distribution does a radioactive decay have?
Which fraction of events do you expect to be larger than 1 second, and how likely is it to have 300 out of 1000 then?
Events should be normally distributed.
Ammm If I understood your question correctly: 300 events should take longer than 1 second. How likely? Am, I would guess with 95% probability.
skrat said:
Events should be normally distributed.
The times of the events? Are you sure?
Ammm If I understood your question correctly: 300 events should take longer than 1 second. How likely? Am, I would guess with 95% probability.
300 is your observed number, I am asking for the prediction. And the 95% is something you will have to compare your result with later.
Well radioactive decay is a completely stochastic process, knowing this I would say it is normally distributed around characteristic time. But I guess it isn't. My next option, which is a result of guessing, would be that the number of decays observed over a given time interval obeys Poission statistics (distribution). If that is the case, than I would highly appreciate a two sentenced explanation, if not than I am lost. :/
Again, I thought that since all events are stochastic and since measurements show that in 30% of the consecutive decays the time is longer than 1 second, it is also my prediction that 30% of number of decays over a given time interval will always be longer than 1 second.
Do you know the concept of half-life? What does it suggest if there is a fixed time during which half of the remaining particles decay?
Ok, I think I understand what I am supposed to do. Please check if this seems to be good.
##N=1000## is the number of decays. Experiment tells us that ##N(1 s<t<2 s)=300## and ##N(t>2 s)=50## therefore ##N(t<1 s)=650##.
Of course $$\frac{dP}{dt}=\frac 1 \tau e^{-\frac t \tau}$$ So the theory for first interval (##t<1s##) predicts $$F_1=\int _0^1\frac 1 \tau e^{-\frac t \tau}=1-e^{-1}=0.6321$$ and similary ##F_2=\int _1^2\frac 2 \tau e^{-\frac t \tau}=e^{-1}-e^{-2}=0.232## and ##F_3=\int _2^\infty\frac 2 \tau e^{-\frac t \tau}=e^{-2}=0.135##.
This now leaves me with $$\chi ^2 =\frac{(650-632)^2}{632}+\frac{(300-232)^2}{232}+\frac{(50-135)^2}{135}=73.9$$ while the data from the tables say that $$\chi ^2(3-1) ^{ 5 \text{%}}=5.9915$$
So I guess the answer is no?
I think the 30% "longer than one second" include the 5% "longer than 2 seconds".
The three values are not uncorrelated (because each event has to be in one of the classes) so you cannot add their ##\chi^2##-contributions like that, but the last term alone is sufficient to draw the same conclusion.
## 1. What is radioactive decay and why is it important to study?
Radioactive decay is the process by which unstable atoms release energy and particles to become more stable. It is important to study because it plays a crucial role in various fields such as nuclear energy, radiometric dating, and medical imaging.
## 2. What does it mean to analyze 1000 events at a 5% risk level?
Analyzing 1000 events at a 5% risk level means that out of 1000 trials, there is a 5% chance of obtaining a result that is due to chance rather than the actual phenomenon being studied. This level of risk is typically used in scientific studies to ensure the reliability of the results.
## 3. How is radioactive decay measured and recorded?
Radioactive decay is measured and recorded using a variety of methods such as counting the number of decay events over a period of time, measuring the decay products, or using specialized instruments like a Geiger counter. The data is then analyzed and recorded in a graph or table for further study.
## 4. What factors can affect the rate of radioactive decay?
The rate of radioactive decay can be affected by various factors such as the type of radioactive material, the temperature, and the presence of other particles. Additionally, external factors such as pressure and electric fields can also influence the rate of decay.
## 5. What are the potential risks of studying radioactive decay?
The potential risks of studying radioactive decay depend on the materials and methods used. In general, there is a risk of exposure to radiation which can have harmful effects on the body. It is important for scientists to follow proper safety protocols and use protective equipment to minimize these risks. | 1,347 | 5,476 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.703125 | 4 | CC-MAIN-2024-10 | latest | en | 0.958514 |
https://math.stackexchange.com/questions/1649562/understanding-basis-algorithm-result | 1,660,813,419,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882573172.64/warc/CC-MAIN-20220818063910-20220818093910-00196.warc.gz | 357,422,020 | 65,482 | # Understanding basis algorithm result
I've a matrix ${\bf A}$ defined as
A = \begin{pmatrix} 1 & -2 & 0 & 3 & 7\\ 2 & 1 & -3 & 1 & 1\\ \end{pmatrix}
And ${W_1}$ is the solution space associated to the homogenous system ${\bf A}$. I am asked to find a basis for ${W_1}$.
I re-wrote the matrix as linear combination of ${c_1}$, i.e.:
\begin{align} x = c_1 + 2 c_2 \\ y = -2c_1+ c_2 \\ z = -3c_2 \\ v = 3c_1 + c_2 \\ w = 7c_1 + c_2 \\ \end{align}
I use these equations to build another matrix, I solve it and then i reach to:
\begin{align} x - \frac{2}{3}y = c_1 \\ x - \frac{-1}{3}z = c_2 \\ 2x + y \frac{-5}{3}z = 0 \\ x - y - v = 0 \\ 3x - 2y - 2 = 0 \end{align}
So, the last three equations are the general ones for $W_1$ and from there I can describe the basis, is this right ?
• Where did you get $c_1, c_2$ from? I think you might benefit from re-writing this as a matrix equation - I'm not certain without seeing more of your working but I think you've approached this back to front. Feb 10, 2016 at 20:31
A standard Gaussian elimination leads to a reduced row echelon form: \begin{align} \begin{pmatrix} 1 & -2 & 0 & 3 & 7\\ 2 & 1 & -3 & 1 & 1 \end{pmatrix} &\to \begin{pmatrix} 1 & -2 & 0 & 3 & 7\\ 0 & 5 & -3 & -5 & -13 \end{pmatrix} &&R_2\gets R_2-2R_1 \\ &\to \begin{pmatrix} 1 & -2 & 0 & 3 & 7\\ 0 & 1 & -3/5 & -1 & -13/5 \end{pmatrix} &&R_2\gets \frac{1}{5}R_2 \\ &\to \begin{pmatrix} 1 & 0 & -6/5 & 1 & 9/5\\ 0 & 1 & -3/5 & -1 & -13/5 \end{pmatrix} &&R_2\gets \frac{1}{5}R_2 \end{align} This means the system is equivalent to $$\begin{cases} x_1=\dfrac{6}{5}x_3-x_4-\dfrac{9}{5}x_5 \\[6px] x_2=\dfrac{3}{5}x_3+x_4+\dfrac{13}{5}x_5 \end{cases}$$ Now it's just a matter of choosing values for $x_3$, $x_4$ and $x_5$ to obtain linearly independent vectors; the choices, in order to also remove denominators, can be $$x_3=5,\quad x_4=0,\quad x_5=0\\ x_3=0,\quad x_4=1,\quad x_5=0\\ x_3=0,\quad x_4=0,\quad x_5=5$$ leading to the three vectors $$\begin{pmatrix}6\\3\\5\\0\\0\end{pmatrix},\quad \begin{pmatrix}-1\\1\\0\\1\\0\end{pmatrix},\quad \begin{pmatrix}-9\\13\\0\\0\\5\end{pmatrix}.$$ These three vectors form a basis for $W_1$.
I can't really follow your reasoning; your equations connecting $x,y,z,v,w$ and $c_1,c_2$ seem inconsistent, and there's that odd appearance of $2$.
One standard way of a getting a basis for $\mathrm{Null}(A)$, i.e. the solution space for $A\mathbf{x}=\mathbf{0}$, is to find the reduced row echelon form of $A$ and just read off the parameterised equations. I'll let you do the calculations for your matrix, but here's a similar example:
$A=\begin{bmatrix}1&2&3&4\\1&4&1&6\end{bmatrix}$, RRE form of $A$ is $\begin{bmatrix}1&0&5&2\\0&1&-1&1\end{bmatrix}$.
The equations from the RRE matrix are $\begin{bmatrix}x_1\\x_2\\x_3\\x_4\end{bmatrix}=\begin{bmatrix}-5x_3&-2x_4\\x_3&-x_4\\x_3\\&x_4\end{bmatrix}=x_2\begin{bmatrix}-5\\1\\1\\0\end{bmatrix}+x_4\begin{bmatrix}-2\\-1\\0\\1\end{bmatrix}$ | 1,212 | 2,944 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 3, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5 | 4 | CC-MAIN-2022-33 | latest | en | 0.69397 |
https://cs50.stackexchange.com/questions/2188/i-used-a-for-loop-for-greedy-but-it-always-gives-0/2195#2195 | 1,642,622,811,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320301488.71/warc/CC-MAIN-20220119185232-20220119215232-00575.warc.gz | 240,762,512 | 25,181 | I used a for loop for greedy but it always gives 0
I wrote greedy in more than one way (`while` loops, modulo) and then I tried a `for` loop which always gives `0` and I don't understand why! Below is the `for` loop, can any one tell me what is wrong with it?
``````for (i=change2; i==0; i=change2)
{
if (change2>=25)
{
change2=change2-25;
n=n+1;
}
else if (change2<25&&change2>=10)
{
change2=change2-10;
n=n+1;
}
else if (change2<10&&change2>=5)
{
change2=change2-5;
n=n+1;
}
else if (change2<5&&change2>=1)
{
change2=change2-1;
n=n+1;
}
}
``````
I think the test condition in the for loop should be like this
``````for (i = change2 ; i > 0 ; i = change2)
{
// do something here
}
``````
because when you write `i == 0`, then the loop executes only when `i` is initialized 0, i.e.`change2` is 0. However `change2` possesses a positive value most of the times. Therefore, using `i > 0`, will do the work as it will iterate the loop till the change is non negative. Remember not to use `i >= 0` because this will lead to an infinite loop as you don't have a escape condition when `i` is equal to 0.
• That worked ! Thanks. Aug 9 '14 at 3:32
• @MohamedAlaaEl-DinFathy Please remember to mark the answer as accepted if it helped you :) Aug 11 '14 at 22:43
Your for loop declaration is quite a mess (sorry), won't be better to use a while loop (while) change2 is higher than 0? | 440 | 1,380 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2022-05 | latest | en | 0.871543 |
http://forums.wolfram.com/mathgroup/archive/2011/Nov/msg00592.html | 1,723,628,987,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641107917.88/warc/CC-MAIN-20240814092848-20240814122848-00693.warc.gz | 10,084,173 | 7,950 | Non trivial substitution in a very long output
• To: mathgroup at smc.vnet.net
• Subject: [mg123132] Non trivial substitution in a very long output
• From: Demind <demind at gmail.com>
• Date: Thu, 24 Nov 2011 06:56:33 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
```Hello, my name is Marco. I am experiencing an annoying problem using Mathematica. I am dealing with a huge expression, some hundreds of lines. I can find 3/4 patterns repeating inside it, and I would really like to substitute thme with dummy variables, namely D1, D2, D3, D4. I'm expecting the readibility of the equation to be improved after this process. As it is right now, it's totally unreadable. I went through past topics to find solutions to my problem, but unfortunately none of the tricks I tried worked (mainly /. and //.).
I give you a sample of what I would like to do, hoping that someone will give me some help:
In my equation, Out[1] = ...
the following pattern is repeated:
Abs[b41]^2 + Abs[b51]^2 + Abs[b61]^2 + Abs[(b61 x1 + b51 x2 + b41 x3)/x4]^2 + Abs[(b61 x2 + b51 x3 + b41 x4)/x1]^2 + Abs[(b61 x1 x3 + b51 (x2 x3 - x1 x4) + b41 (x3^2 - x2 x4))/x4^2]^2 + Abs[(b61 (x1 x3^2 - x1 x2 x4) + b51 (x2 x3^2 - x2^2 x4 - x1 x3 x4) + b41 (x3^3 - 2 x2 x3 x4 + x1 x4^2))/x4^3]^2
I'm doing:
Out[1] //. Abs[b41]^2 + Abs[b51]^2 + Abs[b61]^2 + Abs[(b61 x1 + b51 x2 + b41 x3)/x4]^2 + Abs[(b61 x2 + b51 x3 + b41 x4)/x1]^2 + Abs[(b61 x1 x3 + b51 (x2 x3 - x1 x4) + b41 (x3^2 - x2 x4))/x4^2]^2 + Abs[(b61 (x1 x3^2 - x1 x2 x4) + b51 (x2 x3^2 - x2^2 x4 - x1 x3 x4) + b41 (x3^3 - 2 x2 x3 x4 + x1 x4^2))/x4^3]^2 -> D1
Here the text is attached in "InputForm", where in my notebook I have it in "StandardForm" (I use the latter in my notebook, but here I can't reproduce it for obvious reasons). I tried to use the command above both in StandardForm and in InputForm with no result.
Thank you very much
Marco
```
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• Next by thread: Re: Non trivial substitution in a very long output | 757 | 2,144 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.296875 | 3 | CC-MAIN-2024-33 | latest | en | 0.893219 |
https://www.answers.com/Q/What_do_you_mean_by_relative_density | 1,709,042,735,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474676.26/warc/CC-MAIN-20240227121318-20240227151318-00748.warc.gz | 634,672,299 | 47,355 | 0
# What do you mean by relative density?
Updated: 9/21/2023
Wiki User
11y ago
Use a container of a particular size (say 1 cubic metre) fill with water and weigh.
The weight (mass) = 1000 kg, so density of water = 1000 kg per cubic metre
>
Repeat with iron = 7850 kilograms, so density = 7850 kg per cubic metre
For the same volume iron is 7.85 times the mass of water
So iron is 7.85 times the density of water
Relative density is the density of a material compared to the density of water.
Wiki User
11y ago | 144 | 522 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.625 | 4 | CC-MAIN-2024-10 | latest | en | 0.811238 |
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